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

%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)} C(n-5k,3k).

%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/(1-3x-3x^2-x^3-x^8).

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

%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

%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 February 23 17:23 EST 2018. Contains 299584 sequences. (Running on oeis4.)