Question

Find the solution of the recurrence relation $a_{n}=a_{n - 1} +2a_{n-2}$, $n > 2$ with $a_0 = 0$, $a_1 = 1$.

score 142 · Answer 1 · 2026-04-17 02:58:00

142

Views

Find the solution of the recurrence relation $a_{n}=a_{n - 1} +2a_{n-2}$, $n > 2$ with $a_0 = 0$, $a_1 = 1$.

Published on 17 Apr 2026 - 2:58

score 120 · Answer 2 · 2026-04-16 16:02:06

120

Views

Prove that $a_n = \sum_{k=0}^{\lfloor n/2\rfloor} 1/(k+1) {2k\choose k} {n\choose 2k}$

Published on 16 Apr 2026 - 16:02

score 121 · Answer 3 · 2026-04-17 13:02:33

121

Views

$\lfloor a^m\rfloor \equiv -1\mod n $ for $a = n+\sqrt{n^2 - n}$

Published on 17 Apr 2026 - 13:02

score 50 · Answer 4 · 2026-04-21 20:54:35

50

Views

Definition of chaos: R.May's science paper (1974)

Published on 21 Apr 2026 - 20:54

score 51 · Answer 5 · 2026-04-12 00:05:50

51

Views

general form to big o notation - recurrences

Published on 12 Apr 2026 - 0:05

score 95 · Answer 6 · 2026-04-12 09:27:25

95

Views

solving generating function with non-constant coefficient

Published on 12 Apr 2026 - 9:27

score 73 · Answer 7 · 2026-04-17 09:03:51

73

Views

Prove $T(n)=10T(\dfrac{n}{3})+n\sqrt{n}=\Theta(n^{\log{10}_3})$ using induction

Published on 17 Apr 2026 - 9:03

score 45 · Answer 8 · 2026-04-17 12:25:35

45

Views

find $f(n)$ for recurrence $T(n)=2T(\dfrac{n}{2})+\mathcal{O}(n\log{n})=\Theta(f(n))$

Published on 17 Apr 2026 - 12:25

score 54 · Answer 9 · 2026-04-14 05:41:23

54

Views

Analogue of Lie Theory/Galois theory for Recurrence Relations

Published on 14 Apr 2026 - 5:41

score 80 · Answer 10 · 2026-04-11 03:47:38

80

Views

Proof the equation has only one solution

Published on 11 Apr 2026 - 3:47

score 140 · Answer 11 · 2026-04-13 08:30:28

140

Views

What should the $\mathfrak{sl}(3)$ Chebyshev polynomials be?

Published on 13 Apr 2026 - 8:30

score 59 · Answer 12 · 2026-04-12 08:15:50

59

Views

Non-homogeneous bessel recurrence relation

Published on 12 Apr 2026 - 8:15

score 113 · Answer 13 · 2026-04-16 11:08:49

113

Views

Is there a direct connection between Viète's formula and the sequence $a_{n+1}= a_n +\sqrt{a_n^2 +1}$ ($\lim_{n \to \infty } \frac{a_n}{c_n}=1$)?

Published on 16 Apr 2026 - 11:08

score 123 · Answer 14 · 2026-04-16 17:28:57

123

Views

Solve generating function in recurring form

Published on 16 Apr 2026 - 17:28

score 67 · Answer 15 · 2026-04-09 21:53:15

67

Views

Simplifying a recursive function with 2 variables

Published on 09 Apr 2026 - 21:53

List Question

Find the solution of the recurrence relation $a_{n}=a_{n - 1} +2a_{n-2}$, $n > 2$ with $a_0 = 0$, $a_1 = 1$.

Prove that $a_n = \sum_{k=0}^{\lfloor n/2\rfloor} 1/(k+1) {2k\choose k} {n\choose 2k}$

$\lfloor a^m\rfloor \equiv -1\mod n $ for $a = n+\sqrt{n^2 - n}$

Definition of chaos: R.May's science paper (1974)

general form to big o notation - recurrences

solving generating function with non-constant coefficient

Prove $T(n)=10T(\dfrac{n}{3})+n\sqrt{n}=\Theta(n^{\log{10}_3})$ using induction

find $f(n)$ for recurrence $T(n)=2T(\dfrac{n}{2})+\mathcal{O}(n\log{n})=\Theta(f(n))$

Analogue of Lie Theory/Galois theory for Recurrence Relations

Proof the equation has only one solution

What should the $\mathfrak{sl}(3)$ Chebyshev polynomials be?

Non-homogeneous bessel recurrence relation

Is there a direct connection between Viète's formula and the sequence $a_{n+1}= a_n +\sqrt{a_n^2 +1}$ ($\lim_{n \to \infty } \frac{a_n}{c_n}=1$)?

Solve generating function in recurring form

Simplifying a recursive function with 2 variables

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