A247907 Expansion of (1 + x) / ((1 - x^4) * (1 - x - x^5)) in powers of x.

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

Author

Michael Somos, Sep 26 2014

Keywords

• nonn
• easy

Examples

			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 + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1,1,-1,1,-1).

Crossrefs

Cf. A003520, A133872, A247918.

Programs

Magma

m:=60; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 +x)/((1-x^4)*(1-x-x^5))));  // G. C. Greubel, Aug 04 2018

Mathematica

CoefficientList[Series[(1 + x)/((1 - x^4) (1 - x - x^5)), {x, 0, 100}], x] (* Vincenzo Librandi, Sep 27 2014 *)

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))};

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.