A095129 a(n) = Jac(n)*(2Jac(n)-1), where Jac(n) = A001045(n).

0, 1, 1, 15, 45, 231, 861, 3655, 14365, 58311, 232221, 932295, 3725085, 14913991, 59639581, 238612935, 954386205, 3817763271, 15270790941, 61084037575, 244335101725, 977343902151, 3909371414301, 15637499638215, 62549981775645, 250199983026631, 1000799864997661

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (4,5,-20,-4,16).

Formula

G.f.: x*(1-3*x+6*x^2)/((1-x^2)*(1-4*x)*(1-4*x^2)).

a(n) = 2*(4^n+1)/9 - 4*(-2)^n/9 - 2^n/3 + (-1)^n/3.

a(n) mod 3 = A095130(n).

E.g.f.: (2*exp(4*x) - 3*exp(2*x) + 2*exp(x) + 3*exp(-x) - 4*exp(-2*x)) / 9. - Amiram Eldar, Feb 20 2026

Mathematica

LinearRecurrence[{4, 5, -20, -4, 16}, {0, 1, 1, 15, 45}, 30] (* Harvey P. Dale, Nov 07 2016 *)

Crossrefs

Cf. A001045, A095130.

Sequence in context: A127069 A346853 A241731 * A219813 A068513 A267079

Adjacent sequences: A095126 A095127 A095128 * A095130 A095131 A095132

Keyword

easy,nonn

Author

Paul Barry, May 29 2004

Status

approved