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

Author

Paul Barry, Aug 24 2004

Keywords

• easy
• nonn

Comments

Partial sums of A052244.

Links

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

Programs

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 *)

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.