A053295 Partial sums of A053739.

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

Offset: 0

Author

Barry E. Williams, Mar 04 2000

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A053739, A014166 and A000045.

Right-hand column 12 of triangle A011794.

Cf. A228074.

Programs

Magma

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

Mathematica

Table[Sum[Binomial[n+6-j, n-2*j], {j, 0, Floor[n/2]}], {n, 0, 50}] (* G. C. Greubel, May 24 2018 *)

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

Formula

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

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

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