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A116560
Expansion of g.f. x*(1+x+x^4+x^5-x^6+x^8+x^9)/(1-2*x^6-x^12).
1
0, 1, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 2, 3, 5, 2, 2, 5, 5, 7, 12, 5, 5, 12, 12, 17, 29, 12, 12, 29, 29, 41, 70, 29, 29, 70, 70, 99, 169, 70, 70, 169, 169, 239, 408, 169, 169, 408, 408, 577, 985, 408, 408, 985, 985, 1393, 2378, 985, 985, 2378, 2378
OFFSET
0,9
FORMULA
From R. J. Mathar, Nov 28 2008: (Start)
a(n) = 2*a(n-6) + a(n-12).
G.f.: x*(1+x+x^4+x^5-x^6+x^8+x^9)/(1-2*x^6-x^12).
a(6*n) = a(6*n+3) = a(6*n+4) = A000129(n).
a(6*n+1) = A001333(n).
a(6*n+2) = a(6*n+5) = A000129(n+1). (End)
MATHEMATICA
CoefficientList[Series[x*(1 + x + x^4 + x^5 - x^6 + x^8 + x^9)/(1 - 2 x^6 - x^12), {x, 0, 50}], x] (* G. C. Greubel, Sep 20 2017 *)
PROG
(PARI) x='x+O('x^50); Vec(x*(1+x+x^4+x^5-x^6+x^8+x^9)/(1-2*x^6-x^12)) \\ G. C. Greubel, Sep 20 2017
CROSSREFS
Sequence in context: A234716 A357383 A181885 * A309224 A103784 A153916
KEYWORD
nonn,easy,less
AUTHOR
Roger L. Bagula, Mar 17 2006
EXTENSIONS
Terms a(37) onward added by G. C. Greubel, Sep 20 2017
Better name using given g.f. from Joerg Arndt, Oct 26 2024
STATUS
approved