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A053295
Partial sums of A053739.
11
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
0,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.
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
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
Right-hand column 12 of triangle A011794.
Cf. A228074.
Sequence in context: A257201 A258475 A320753 * A266939 A055798 A002664
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Mar 04 2000
STATUS
approved