A017853 Expansion of 1/(1-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13).

1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 3, 3, 4, 5, 6, 8, 11, 13, 16, 20, 25, 32, 42, 53, 66, 83, 104, 131, 167, 212, 267, 337, 425, 536, 678, 858, 1083, 1367, 1726, 2179, 2753, 3480, 4396, 5551, 7010, 8852, 11180, 14124

Offset

0,13

Comments

Number of compositions (ordered partitions) of n into parts 6, 7, 8, 9, 10, 11, 12 and 13. - Ilya Gutkovskiy, May 25 2017

Links

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

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

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) for n>12. - Vincenzo Librandi, Jun 28 2013

Mathematica

CoefficientList[Series[1/(1 - Total[(x^Range[6, 13])]), {x, 0, 50}], x] (* Harvey P. Dale, Apr 21 2011 *)
CoefficientList[Series[1 / (1 - x^6 - x^7 - x^8 - x^9 - x^10 - x^11 - x^12 - x^13), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 28 2013 *)

Prog

(Magma) 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))); /* or */ I:=[1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2]; [n le 13 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): n in [1..70]]; // Vincenzo Librandi, Jun 28 2013

Crossrefs

Sequence in context: A355358 A205216 A304885 * A241518 A372593 A125616

Adjacent sequences: A017850 A017851 A017852 * A017854 A017855 A017856

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved