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A053295 Partial sums of A053739. 10
1, 7, 29, 92, 247, 591, 1300, 2683, 5270, 9955, 18228, 32551, 56967, 98086, 166681, 280271, 467301, 773906, 1274856, 2091266, 3419252, 5576298, 9076280, 14750858, 23945893, 38839257, 62955061, 101995694 (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 (7,-20,29,-20,1,8,-5,1).

FORMULA

a(n) = Sum_{i=0..floor(n/2)} C(n+6-i, n-2i), n >= 0.

a(n) = Sum_{k=1..n} C(n-k+6,k+5), with n>=0. - Paolo P. Lava, Apr 16 2008

G.f.: -1 / ( (x^2 + x - 1)*(x-1)^6 ). - R. J. Mathar, Oct 10 2014

EXAMPLE

a(n) = a(n-1) + a(n-2) + C(n+5,5); n >= 0; a(-1)=0.

MATHEMATICA

Table[Sum[Binomial[n+6-j, n-2*j], {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+6-j, n-2*j)), ", ")) \\ G. C. Greubel, May 24 2018

(MAGMA) [(&+[Binomial(n+6-j, n-2*j): j in [0..Floor(n/2)]]): n in [0..30]]; // G. C. Greubel, May 24 2018

CROSSREFS

Cf. A053739, A014166 and A000045.

Right-hand column 12 of triangle A011794.

Cf. A228074.

Sequence in context: A001779 A257201 A258475 * A266939 A055798 A002664

Adjacent sequences:  A053292 A053293 A053294 * A053296 A053297 A053298

KEYWORD

easy,nonn,changed

AUTHOR

Barry E. Williams, Mar 04 2000

STATUS

approved

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Last modified May 26 07:47 EDT 2018. Contains 304593 sequences. (Running on oeis4.)