A097790 a(n)=5a(n-1)+C(n+3,3),n>0, a(0)=1.

1, 9, 55, 295, 1510, 7606, 38114, 190690, 953615, 4768295, 23841761, 119209169, 596046300, 2980232060, 14901160980, 74505805716, 372529029549, 1862645148885, 9313225745755, 46566128730315, 232830643653346

Offset

0,2

Comments

Partial sums of A052244.

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (9,-26,34,-21,5).

Formula

G.f.: 1/((1-5*x)*(1-x)^4).

a(n) = 5^(n+4)/256-(32*n^3+312*n^2+1012*n+1107)/768.

a(n) = Sum_{k=0..n} binomial(n+4, k+4)*4^k.

Mathematica

nxt[{n_, a_}]:={n+1, 5a+Binomial[n+4, 3]}; NestList[nxt, {0, 1}, 20][[All, 2]] (* or *) LinearRecurrence[{9, -26, 34, -21, 5}, {1, 9, 55, 295, 1510}, 30] (* Harvey P. Dale, Sep 20 2022 *)

Crossrefs

Sequence in context: A072844 A026857 A244650 * A356339 A362365 A183805

Adjacent sequences: A097787 A097788 A097789 * A097791 A097792 A097793

Keyword

easy,nonn

Author

Paul Barry, Aug 24 2004

Status

approved