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A053309 Partial sums of A053308. 5
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 (list; graph; refs; listen; history; text; internal format)
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.

a(n) = Sum_{k=1..n} C(n-k+9,k+8), with n>=0. - Paolo P. Lava, Apr 16 2008

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

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Last modified December 5 06:52 EST 2021. Contains 349543 sequences. (Running on oeis4.)