A017865 Expansion of 1/(1-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16).

1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 5, 6, 7, 9, 12, 16, 19, 23, 28, 34, 42, 53, 68, 85, 105, 129, 159, 196, 243, 304, 380, 473, 586, 726, 899, 1114, 1384, 1722, 2142, 2660, 3301, 4095, 5080, 6305, 7831

Offset

0,15

Comments

Number of compositions (ordered partitions) of n into parts 7, 8, 9, 10, 11, 12, 13, 14, 15 and 16. - Ilya Gutkovskiy, May 26 2017

Links

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

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

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=1, a(8)=1, a(9)=1, a(10)=1, a(11)=1, a(12)=1, a(13)=1, a(14)=2, a(15)=3; for n>15, a(n) = 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) +a(n-16). [Harvey P. Dale, Feb 02 2012]

Mathematica

CoefficientList[Series[1/(1 - Total[x^Range[7, 16]]), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 3}, 60] (* Harvey P. Dale, Feb 02 2012 *)

Prog

(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 3]; [n le 16 select I[n] else 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)+Self(n-16): n in [1..60]]; // Vincenzo Librandi, Jun 28 2013

Crossrefs

Sequence in context: A261085 A017876 A356860 * A317143 A351520 A065328

Adjacent sequences: A017862 A017863 A017864 * A017866 A017867 A017868

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved