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A053295
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Partial sums of A053739.
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11
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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
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OFFSET
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0,2
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.
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LINKS
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FORMULA
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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
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MATHEMATICA
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Table[Sum[Binomial[n+6-j, n-2*j], {j, 0, Floor[n/2]}], {n, 0, 50}] (* G. C. Greubel, May 24 2018 *)
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PROG
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(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
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CROSSREFS
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Right-hand column 12 of triangle A011794.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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