Question

Finding closed form of $u_{n+1} =2u_n - n^2$

score 107 · Answer 1 · 2026-04-16 13:16:42

107

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Finding closed form of $u_{n+1} =2u_n - n^2$

Published on 16 Apr 2026 - 13:16

score 149 · Answer 2 · 2026-04-16 07:28:58

149

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Taylor series of $\displaystyle x!_{(\infty)}=\prod_{j=1}^{\infty} j^{\text{sinc}(x-j)}$ - generalization of $\psi(z)$

Published on 16 Apr 2026 - 7:28

score 55 · Answer 3 · 2026-04-10 19:48:08

55

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What is the recurrence relation for this sum?

Published on 10 Apr 2026 - 19:48

score 80 · Answer 4 · 2026-04-15 21:26:15

80

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Could we find the n-th term formula for recursive formula $x_{n+1} = {x_n{({x_n \over {x_n+7}}+43)^3}}$

Published on 15 Apr 2026 - 21:26

score 72 · Answer 5 · 2026-04-12 01:36:15

72

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Pouring fractions of water from a vase to another (recurrence sequence)

Published on 12 Apr 2026 - 1:36

score 64 · Answer 6 · 2026-04-15 16:18:16

64

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Staying alive indefinitely in a game where, at each instance, any entity can only move up, down, left, right, or stay still.

Published on 15 Apr 2026 - 16:18

score 45 · Answer 7 · 2026-04-13 04:50:28

45

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Stanley says $E_{n+1,k+1}=E_{n+1,k}+E_{n,n-k}$ about counting alternating permutations

Published on 13 Apr 2026 - 4:50

score 137 · Answer 8 · 2026-04-11 13:13:22

137

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Proving $x + \sin x + \sin(x + \sin x) + \sin(x + \sin x + \sin(x + \sin x)) + ... = \pi $

Published on 11 Apr 2026 - 13:13

score 84 · Answer 9 · 2026-04-13 20:53:00

84

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Estimating the sum of fourth powers of a recursively defined sequence, $a_{n+1} = a_n - 2a_n^2$ with $a_1 = \beta$

Published on 13 Apr 2026 - 20:53

score 60 · Answer 10 · 2026-04-11 08:35:30

60

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Is every solution of a nonhomogenous linear recurrence also a solution to some homogenous linear recurrence?

Published on 11 Apr 2026 - 8:35

score 24 · Answer 11 · 2026-04-09 07:29:39

24

Views

Solve VAR(2) for the n-step ahead forecast

Published on 09 Apr 2026 - 7:29

score 184 · Answer 12 · 2026-04-14 22:13:14

184

Views

Recurrence relation for $I_n=\int (\sin x+\cos x)^n \,\Bbb dx$

Published on 14 Apr 2026 - 22:13

score 43 · Answer 13 · 2026-04-09 04:50:19

43

Views

From cumulants of a random variable to its moments

Published on 09 Apr 2026 - 4:50

score 55 · Answer 14 · 2026-04-16 14:23:15

55

Views

$A\subset \mathbb{N}$ and $(A+1)=\{x+1\mid x\in A\}$. how many subsets of $\{1,2,3,\dots, n\}$ exists, such that $A\cup(A+1)=\{1,2,3,\dots, n+1\}$.

Published on 16 Apr 2026 - 14:23

score 49 · Answer 15 · 2026-04-16 19:46:53

49

Views

Make a new sequence (bn) by swapping values a0 and a1 of an old sequence (an) then figure out the closed sequence for bn

Published on 16 Apr 2026 - 19:46

List Question

Finding closed form of $u_{n+1} =2u_n - n^2$

Taylor series of $\displaystyle x!_{(\infty)}=\prod_{j=1}^{\infty} j^{\text{sinc}(x-j)}$ - generalization of $\psi(z)$

What is the recurrence relation for this sum?

Could we find the n-th term formula for recursive formula $x_{n+1} = {x_n{({x_n \over {x_n+7}}+43)^3}}$

Pouring fractions of water from a vase to another (recurrence sequence)

Staying alive indefinitely in a game where, at each instance, any entity can only move up, down, left, right, or stay still.

Stanley says $E_{n+1,k+1}=E_{n+1,k}+E_{n,n-k}$ about counting alternating permutations

Proving $x + \sin x + \sin(x + \sin x) + \sin(x + \sin x + \sin(x + \sin x)) + ... = \pi $

Estimating the sum of fourth powers of a recursively defined sequence, $a_{n+1} = a_n - 2a_n^2$ with $a_1 = \beta$

Is every solution of a nonhomogenous linear recurrence also a solution to some homogenous linear recurrence?

Solve VAR(2) for the n-step ahead forecast

Recurrence relation for $I_n=\int (\sin x+\cos x)^n \,\Bbb dx$

From cumulants of a random variable to its moments

$A\subset \mathbb{N}$ and $(A+1)=\{x+1\mid x\in A\}$. how many subsets of $\{1,2,3,\dots, n\}$ exists, such that $A\cup(A+1)=\{1,2,3,\dots, n+1\}$.

Make a new sequence (bn) by swapping values a0 and a1 of an old sequence (an) then figure out the closed sequence for bn

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