A017846 Expansion of 1/(1-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15).

1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 8, 10, 14, 19, 25, 33, 42, 55, 73, 97, 129, 169, 221, 290, 382, 505, 666, 877, 1153, 1516, 1996, 2629, 3464, 4562, 6005, 7904, 10404, 13699, 18040, 23755, 31277, 41176

Offset

0,11

Comments

Number of compositions of n into parts p where 5 <= p <= 15. [Joerg Arndt, Jun 27 2013]

Links

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

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

Formula

a(n) = a(n-5) +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) +a(n-15) for n>14. - Vincenzo Librandi, Jun 27 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[5, 15]]), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 27 2013 *)
LinearRecurrence[{0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6}, 50] (* Harvey P. Dale, Sep 20 2023 *)

Prog

(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15))); /* or */ I:=[1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6]; [n le 15 select I[n] else Self(n-5)+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)+Self(n-15): n in [1..70]]; // Vincenzo Librandi, Jun 27 2013

Crossrefs

Sequence in context: A269303 A276642 A320317 * A179053 A218949 A129976

Adjacent sequences: A017843 A017844 A017845 * A017847 A017848 A017849

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved