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 A113032 a(n) = Sum_{k=0..floor(n/8)} binomial(n-5*k, 3*k). 1
 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 21, 36, 57, 85, 121, 167, 228, 315, 449, 666, 1023, 1605, 2533, 3974, 6156, 9394, 14137, 21051, 31159, 46066, 68305, 101850, 152857, 230720, 349576, 530476, 804579, 1217951, 1838897, 2769267, 4161918, 6247570, 9375799 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 R. Austin and R. K. Guy, Binary sequences without isolated ones, Fib. Quart., 16 (1978), 84-86. FORMULA G.f.: (1-x)^2/(1-3*x-3*x^2-x^3-x^8). EXAMPLE a(10+1)=11 because C(10,0) + C(5,3) = 1+10 = 11. MATHEMATICA Table[Sum[Binomial[n - 5*k, 3*k], {k, 0, Floor[n/8]}], {n, 0, 50}] (* G. C. Greubel, Apr 09 2018 *) PROG (PARI) a(n) = sum(k=0, n\8, binomial(n-5*k, 3*k)); \\ Michel Marcus, Sep 05 2013 (PARI) lista(nn) = {my(x = xx + O(xx^nn)); gf = (1-x)^2/(1-3*x-3*x^2-x^3-x^8); for (i=0, nn-1, print1(polcoeff(gf, i, xx), ", ")); } \\ Michel Marcus, Sep 05 2013 (MAGMA) [(&+[Binomial(n-5*k, 3*k): k in [0..Floor(n/8)]]): n in [0..50]]; // G. C. Greubel, Apr 09 2018 CROSSREFS Cf. A005251, A005253, A000045. Sequence in context: A005575 A294745 A050407 * A100134 A137356 A103198 Adjacent sequences:  A113029 A113030 A113031 * A113033 A113034 A113035 KEYWORD nonn AUTHOR Alexey Kistanov (plast(AT)solid.ru), Jan 05 2006 EXTENSIONS Corrected by T. D. Noe, Nov 01 2006 More terms from Michel Marcus, Sep 05 2013 STATUS approved

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)