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 A113032 a(n) = Sum_{k=0..floor(n/8)} binomial(n-5*k, 3*k). 1

%I

%S 1,1,1,1,1,1,1,1,2,5,11,21,36,57,85,121,167,228,315,449,666,1023,1605,

%T 2533,3974,6156,9394,14137,21051,31159,46066,68305,101850,152857,

%U 230720,349576,530476,804579,1217951,1838897,2769267,4161918,6247570,9375799

%N a(n) = Sum_{k=0..floor(n/8)} binomial(n-5*k, 3*k).

%H G. C. Greubel, <a href="/A113032/b113032.txt">Table of n, a(n) for n = 0..5000</a>

%H R. Austin and R. K. Guy, <a href="http://www.fq.math.ca/Scanned/16-1/austin.pdf">Binary sequences without isolated ones</a>, Fib. Quart., 16 (1978), 84-86.

%F G.f.: (1-x)^2/(1-3*x-3*x^2-x^3-x^8).

%e a(10+1)=11 because C(10,0) + C(5,3) = 1+10 = 11.

%t Table[Sum[Binomial[n - 5*k, 3*k], {k, 0, Floor[n/8]}], {n, 0, 50}] (* _G. C. Greubel_, Apr 09 2018 *)

%o (PARI) a(n) = sum(k=0, n\8, binomial(n-5*k, 3*k)); \\ _Michel Marcus_, Sep 05 2013

%o (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

%o (MAGMA) [(&+[Binomial(n-5*k, 3*k): k in [0..Floor(n/8)]]): n in [0..50]]; // _G. C. Greubel_, Apr 09 2018

%Y Cf. A005251, A005253, A000045.

%K nonn

%O 0,9

%A Alexey Kistanov (plast(AT)solid.ru), Jan 05 2006

%E Corrected by _T. D. Noe_, Nov 01 2006

%E More terms from _Michel Marcus_, Sep 05 2013

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Last modified August 21 02:08 EDT 2018. Contains 313930 sequences. (Running on oeis4.)