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A097790
a(n)=5a(n-1)+C(n+3,3),n>0, a(0)=1.
2
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.
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Aug 24 2004
STATUS
approved