Question

Why does the difference equation $x_nx_{n+2}=w^5x_n-(w^2+w^3)x_{n+1}+x_{n+2}$ generate cyclic sequences?

score 255 · Answer 1 · 2020-05-01 08:42:55

255

Views

Why does the difference equation $x_nx_{n+2}=w^5x_n-(w^2+w^3)x_{n+1}+x_{n+2}$ generate cyclic sequences?

Published on 01 May 2020 - 8:42

score 98 · Answer 2 · 2020-05-01 09:50:32

98

Views

How can I solve this basic recurrence $T(n) = \sqrt{n} \cdot T(\sqrt{n}) + n^2$?

Published on 01 May 2020 - 9:50

score 39 · Answer 3 · 2026-03-25 07:47:34

39

Views

Inconsistent formulas when solving recurrent equations using sympy.rsolve_poly

Published on 25 Mar 2026 - 7:47

score 65 · Answer 4 · 2026-04-03 04:49:56

65

Views

Does every sequence $s_{i+1} := \text{gpf}(s_{i}^2+k)$ eventually cycle?

Published on 03 Apr 2026 - 4:49

score 44 · Answer 5 · 2020-05-01 21:50:07

44

Views

Computing an arbitrary number of sums of sums

Published on 01 May 2020 - 21:50

score 96 · Answer 6 · 2026-02-24 14:24:53

96

Views

Quadratic Recurrence $a_{n+1} = 4a_n - 4a_n^2$

Published on 24 Feb 2026 - 14:24

score 94 · Answer 7 · 2026-02-24 14:28:20

94

Views

Let $f : \mathbb R^+ \rightarrow \mathbb R^+$ satisfies $f(f(x)) + f(x) = 6x$. Show that $f(x) = 2x$ only.

Published on 24 Feb 2026 - 14:28

score 66 · Answer 8 · 2020-05-03 06:38:09

66

Views

Closed form of $a_{n+1} = a_n^2 - 2$

Published on 03 May 2020 - 6:38

score 333 · Answer 9 · 2026-03-31 05:14:21

333

Views

Closed form of recurrence relation $a_k=(n+k)a_{k-1}-ka_{k-2}$

Published on 31 Mar 2026 - 5:14

score 54 · Answer 10 · 2020-05-04 07:46:02

54

Views

Combinatorics and Recurrence Relationship

Published on 04 May 2020 - 7:46

score 186 · Answer 11 · 2020-05-04 17:01:00

186

Views

particular solution of recurrence relation help

Published on 04 May 2020 - 17:01

score 28 · Answer 12 · 2020-05-04 22:27:32

28

Views

solving recursion relation but need to prove that x_n is real

Published on 04 May 2020 - 22:27

score 65 · Answer 13 · 2026-04-08 12:50:07

65

Views

General formula of recursive sequence

Published on 08 Apr 2026 - 12:50

score 1.3k · Answer 14 · 2026-03-26 10:43:36

1.3k

Views

Determine the number of $n$-digit quaternary $\{0,1,2,3\}$ sequences $a_n$ in which there is never a $3$ anywhere to the right of a $0$.

Published on 26 Mar 2026 - 10:43

score 797 · Answer 15 · 2026-03-26 04:29:17

797

Views

Recurrence relations for annuities

Published on 26 Mar 2026 - 4:29

List Question

Why does the difference equation $x_nx_{n+2}=w^5x_n-(w^2+w^3)x_{n+1}+x_{n+2}$ generate cyclic sequences?

How can I solve this basic recurrence $T(n) = \sqrt{n} \cdot T(\sqrt{n}) + n^2$?

Inconsistent formulas when solving recurrent equations using sympy.rsolve_poly

Does every sequence $s_{i+1} := \text{gpf}(s_{i}^2+k)$ eventually cycle?

Computing an arbitrary number of sums of sums

Quadratic Recurrence $a_{n+1} = 4a_n - 4a_n^2$

Let $f : \mathbb R^+ \rightarrow \mathbb R^+$ satisfies $f(f(x)) + f(x) = 6x$. Show that $f(x) = 2x$ only.

Closed form of $a_{n+1} = a_n^2 - 2$

Closed form of recurrence relation $a_k=(n+k)a_{k-1}-ka_{k-2}$

Combinatorics and Recurrence Relationship

particular solution of recurrence relation help

solving recursion relation but need to prove that x_n is real

General formula of recursive sequence

Determine the number of $n$-digit quaternary $\{0,1,2,3\}$ sequences $a_n$ in which there is never a $3$ anywhere to the right of a $0$.

Recurrence relations for annuities

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