A053308 Partial sums of A053296.

1, 9, 46, 175, 551, 1518, 3785, 8735, 18955, 39130, 77533, 148487, 276408, 502415, 895103, 1568062, 2708322, 4622488, 7811510, 13091798, 21791338, 36067176, 59419294, 97522270, 159571139, 260459265, 424302452, 690141333

Offset

0,2

References

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-35,76,-98,70,-14,-20,19,-7,1).

Formula

a(n) = Sum_{i=0..floor(n/2)} C(n+8-i, n-2i), n >= 0.

a(n) = a(n-1) + a(n-2) + C(n+7,7); n >= 0; a(-1)=0.

Mathematica

Table[Sum[Binomial[n+8-j, n-2j], {j, 0, Floor[n/2]}], {n, 0, 50}] (* G. C. Greubel, May 24 2018 *)

Prog

(PARI) for(n=0, 30, print1(sum(j=0, floor(n/2), binomial(n+8-j, n-2*j)), ", ")) \\ G. C. Greubel, May 24 2018
(Magma) [(&+[Binomial(n+8-j, n-2*j): j in [0..Floor(n/2)]]): n in [0..30]]; // G. C. Greubel, May 24 2018

Crossrefs

Cf. A053296, A053295, A136431.

Cf. A228074.

Sequence in context: A001781 A258477 A320755 * A201458 A034487 A035039

Adjacent sequences: A053305 A053306 A053307 * A053309 A053310 A053311

Keyword

easy,nonn

Author

Barry E. Williams, Mar 06 2000

Status

approved