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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.)