A017837 Expansion of 1/(1 - x^5 - x^6).

1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 3, 3, 1, 0, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 2, 6, 15, 20, 15, 7, 8, 21, 35, 35, 22, 15, 29, 56, 70, 57, 37, 44, 85, 126, 127, 94, 81, 129, 211, 253, 221, 175, 210, 340, 464, 474, 396, 385, 550, 804, 938, 870, 781, 935, 1354, 1742, 1808, 1651, 1716, 2289, 3096

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions of n into parts 5 and 6. - Joerg Arndt, Jun 27 2013

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vincenzo Librandi)
• Johann Cigler, Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials, arXiv:2212.02118 [math.NT], 2022.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,1).

Crossrefs

Column 5 of A306713.

Cf. A099132.

Programs

Magma

m:=70; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^5-x^6))); // Vincenzo Librandi, Jun 27 2013

Magma

I:=[1,0,0,0,0,1]; [n le 6 select I[n] else Self(n-5)+Self(n-6): n in [1..70]]; // Vincenzo Librandi, Jun 27 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[5, 6]]), {x, 0, 50}], x] (* Vincenzo Librandi Jun 27 2013 *)

PARI

Vec(1/(1-x^5-x^6)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = a(n-6) + a(n-5). - Jon E. Schoenfield, Aug 07 2006