%I #16 Feb 07 2023 15:12:51

%S 1,1,9,25,97,321,1097,3641,12033,39361,127945,413337,1328609,4251521,

%T 13551753,43046713,136314625,430467201,1355971721,4261625369,

%U 13366006881,41841412801,130754415049,407953774905,1270932914177

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

%H Harvey P. Dale, <a href="/A083672/b083672.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,2,-12,-9).

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

%F O.g.f.: -(x - 1)^3/((-1 + 3*x)^2*(1 + x)^2). - _R. J. Mathar_, Apr 02 2008

%F E.g.f.: exp(x)*(cosh(2*x) + x*sinh(2*x)). - _Stefano Spezia_, Aug 04 2022

%t LinearRecurrence[{4,2,-12,-9},{1,1,9,25},30] (* _Harvey P. Dale_, Feb 07 2023 *)

%Y Cf. A002697, A045891.

%K easy,nonn

%O 0,3

%A _Paul Barry_, May 02 2003