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.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,1).
FORMULA
G.f.: (1-x)^2/(1-3*x+3*x^2-x^3-x^8). [corrected by Georg Fischer, Apr 17 2020]
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
(Sage) ((1-x)^2/(1-3*x+3*x^2-x^3-x^8)).series(x, 44).coefficients(x, sparse=False) # Stefano Spezia, Aug 19 2023
CROSSREFS
KEYWORD
nonn,easy
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