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

0,3

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).

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

Mathematica

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

Crossrefs

Cf. A002697, A045891.

Sequence in context: A147460 A147475 A146674 * A193644 A083100 A084058

Adjacent sequences: A083669 A083670 A083671 * A083673 A083674 A083675

Keyword

easy,nonn

Author

Paul Barry, May 02 2003

Status

approved