A364636 - OEIS

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A364636

a(n) = ((1 - sqrt(2))^n + (1 + sqrt(2))^n)*n/2.

2

0, 1, 6, 21, 68, 205, 594, 1673, 4616, 12537, 33630, 89309, 235212, 615173, 1599402, 4137105, 10653712, 27327857, 69856182, 178017061, 452390740, 1146776253, 2900399106, 7320463897, 18441561624, 46376946025, 116442406158, 291929022189, 730881930716, 1827523107829

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Paolo Xausa, Table of n, a(n) for n = 0..2500

Index entries for linear recurrences with constant coefficients, signature (4,-2,-4,-1).

FORMULA

The sequence can be continued to all ZZ, and a(-n) = -(-1)^n*a(n).

a(n) = [x^n] (x + 2*x^2 - x^3)/(-1 + x*(2 + x))^2.

a(n) = 2*A364553(n) - A093967(n).

MAPLE

A364636 := n -> ((1 - sqrt(2))^n + (1 + sqrt(2))^n)*n / 2:

seq(simplify(A364636(n)), n = 0..29);

MATHEMATICA

A364636[n_] := n*(Fibonacci[n+1, 2] - Fibonacci[n, 2]); Array[A364636, 30, 0] (* or *)

LinearRecurrence[{4, -2, -4, -1}, {0, 1, 6, 21}, 30] (* Paolo Xausa, Jan 25 2026 *)

PROG

(PARI) a(n) = ((1 - quadgen(8))^n + (1 + quadgen(8))^n)*n/2; \\ Michel Marcus, Jul 31 2023

CROSSREFS

Cf. A093967, A364553.

Sequence in context: A107653 A123653 A375297 * A318943 A200761 A169687

Adjacent sequences: A364633 A364634 A364635 * A364637 A364638 A364639

KEYWORD

nonn,easy

AUTHOR

Peter Luschny, Jul 30 2023

STATUS

approved