A017891 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 2, 3, 6, 10, 15, 21, 25, 27, 27, 25, 22, 19, 20, 26, 38, 57, 80, 104, 125, 140, 147, 145, 140, 139, 150, 182, 240, 325, 430, 544, 653

Offset

0,22

Comments

Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14 and 15. - Ilya Gutkovskiy, May 27 2017

Links

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

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

Formula

a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) for n>14. - Vincenzo Librandi, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[10, 15]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jul 01 2013 *)

Prog

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14-x^15))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]; [n le 15 select I[n] else Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15): n in [1..70]]; // Vincenzo Librandi, Jul 01 2013

Crossrefs

Sequence in context: A271859 A232240 A073793 * A017881 A017871 A366259

Adjacent sequences: A017888 A017889 A017890 * A017892 A017893 A017894

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved