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

Offset: 0

Author

Peter Luschny, Jul 30 2023

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A093967, A364553.

Programs

Maple

A364636 := n -> ((1 - sqrt(2))^n + (1 + sqrt(2))^n)*n / 2:
seq(simplify(A364636(n)), n = 0..29);

PARI

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

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).