A053309 Partial sums of A053308.

1, 10, 56, 231, 782, 2300, 6085, 14820, 33775, 72905, 150438, 298925, 575333, 1077748, 1972851, 3540913, 6249235, 10871723, 18683233, 31775031, 53566369, 89633545, 149052839, 246575109, 406146248, 666605513, 1090907965

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 (10,-44,111,-174,168,-84,-6,39,-26,8,-1).

Formula

a(n) = Sum_{i=0..floor(n/2)} C(n+9-i, n-2i), n >= 0.

a(n) = a(n-1) + a(n-2) + C(n+8,8); n >= 0; a(-1)=0.

G.f.: 1/((x^2 + x - 1)*(x-1)^9). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009

Mathematica

Table[Sum[Binomial[n+9-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+9-j, n-2*j)), ", ")) \\ G. C. Greubel, May 24 2018
(Magma) [(&+[Binomial(n+9-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: A001786 A258478 A320756 * A035040 A002889 A055911

Adjacent sequences: A053306 A053307 A053308 * A053310 A053311 A053312

Keyword

easy,nonn

Author

Barry E. Williams, Mar 06 2000

Status

approved