A017819 Expansion of 1/(1-x^3-x^4-x^5-x^6).

1, 0, 0, 1, 1, 1, 2, 2, 3, 5, 6, 8, 12, 16, 22, 31, 42, 58, 81, 111, 153, 212, 292, 403, 557, 768, 1060, 1464, 2020, 2788, 3849, 5312, 7332, 10121, 13969, 19281, 26614, 36734, 50703, 69985, 96598, 133332, 184036, 254020, 350618, 483951, 667986, 922006, 1272625, 1756575, 2424561, 3346568, 4619192, 6375767, 8800329, 12146896

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions of n into parts 3, 4, 5, and 6. - David Neil McGrath, Aug 17 2014

Links

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

Crossrefs

Cf. A137200.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^3-x^4-x^5-x^6)))); // Vincenzo Librandi, Jun 27 2013

Magma

I:=[1,0,0,1,1,1]; [n le 6 select I[n] else Self(n-3)+Self(n-4)+Self(n-5)+Self(n-6): n in [1..50]]; // Vincenzo Librandi, Jun 27 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[3, 6]]), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 27 2013 *)
LinearRecurrence[{0,0,1,1,1,1},{1,0,0,1,1,1},50] (* Harvey P. Dale, Aug 15 2014 *)

PARI

Vec(1/(1-x^3-x^4-x^5-x^6)+ O(x^60)) \\ Michel Marcus, Aug 17 2014

Formula

a(n) = a(n-6) + a(n-5) + a(n-4) + a(n-3). - Jon E. Schoenfield, Aug 07 2006

a(n) = a(n-1) + a(n-4) + {1, -1, or 0} depending on whether n mod 3 is {0, 1, or 2}. - Barry Cipra, Mar 03 2008