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A247907
Expansion of (1 + x) / ((1 - x^4) * (1 - x - x^5)) in powers of x.
3
1, 2, 2, 2, 3, 5, 7, 9, 12, 16, 21, 28, 38, 51, 67, 88, 117, 156, 207, 274, 363, 481, 637, 844, 1119, 1483, 1964, 2601, 3446, 4566, 6049, 8013, 10615, 14062, 18628, 24677, 32691, 43307, 57369, 75997, 100675, 133367, 176674, 234043, 310041, 410717, 544084
OFFSET
0,2
FORMULA
G.f.: 1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 - x^2 - x^3)).
a(n) = -A247918(-8-n) for all n in Z.
Convolution of A003520 and A133872.
0 = a(n) + a(n+4) - a(n+5) + mod(floor((n-1) / 2), 2) for all n in Z.
0 = a(n) - a(n+1) + a(n+2) - a(n+3) + a(n+4) - 2*a(n+5) + 2*a(n+6) - 2*a(n+7) + a(n+8) for all n in Z.
EXAMPLE
G.f. = 1 + 2*x + 2*x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 7*x^6 + 9*x^7 + 12*x^8 + ...
MATHEMATICA
CoefficientList[Series[(1 + x)/((1 - x^4) (1 - x - x^5)), {x, 0, 100}], x] (* Vincenzo Librandi, Sep 27 2014 *)
PROG
(PARI) {a(n) = if( n<0, n=-8-n; polcoeff( -1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 + x - x^3)) + x * O(x^n), n), polcoeff( 1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 - x^2 - x^3)) + x * O(x^n), n))};
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 +x)/((1-x^4)*(1-x-x^5)))); // G. C. Greubel, Aug 04 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Somos, Sep 26 2014
STATUS
approved