A017854 Expansion of 1/(1-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14).

1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 5, 6, 8, 11, 15, 18, 22, 27, 34, 44, 58, 74, 93, 116, 146, 185, 237, 303, 385, 486, 614, 777, 987, 1256, 1597, 2025, 2565, 3249, 4120, 5230, 6642, 8430, 10692, 13556, 17190

Offset

0,13

Comments

Number of compositions of n into parts p where 6 <= p <= 14. [Joerg Arndt, Jun 28 2013]

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1,1,1,1,1,1,1,1,1).

Formula

a(n) = a(n-6) +a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) for n>13. - Vincenzo Librandi, Jun 28 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[6, 14]]), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 28 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 3}, 60] (* Harvey P. Dale, Apr 16 2024 *)

Prog

(Magma) I:=[1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 3]; [n le 14 select I[n] else Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14): n in [1..70]]; /* or */ m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14))); // Vincenzo Librandi, Jun 28 2013

Crossrefs

Sequence in context: A015737 A015745 A375476 * A261171 A330264 A356208

Adjacent sequences: A017851 A017852 A017853 * A017855 A017856 A017857

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved