A083672 Binomial transform of 1,8,48,256,1280,6144,... (cf. A002697).

1, 1, 9, 25, 97, 321, 1097, 3641, 12033, 39361, 127945, 413337, 1328609, 4251521, 13551753, 43046713, 136314625, 430467201, 1355971721, 4261625369, 13366006881, 41841412801, 130754415049, 407953774905, 1270932914177

Offset: 0

Author

Paul Barry, May 02 2003

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,2,-12,-9).

Crossrefs

Cf. A002697, A045891.

Programs

Mathematica

LinearRecurrence[{4,2,-12,-9},{1,1,9,25},30] (* Harvey P. Dale, Feb 07 2023 *)

Formula

a(n) = (1/6)*((n + 3)*3^n + (3*n + 3)*(-1)^n).

O.g.f.: -(x - 1)^3/((-1 + 3*x)^2*(1 + x)^2). - R. J. Mathar, Apr 02 2008

E.g.f.: exp(x)*(cosh(2*x) + x*sinh(2*x)). - Stefano Spezia, Aug 04 2022