A017849 Expansion of 1/(1-x^6-x^7-x^8-x^9).

1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 3, 4, 3, 2, 2, 3, 6, 10, 12, 12, 11, 10, 13, 21, 31, 40, 45, 45, 46, 55, 75, 105, 137, 161, 176, 191, 221, 281, 372, 478, 579, 665, 749, 869, 1065, 1352, 1710, 2094, 2471, 2862

Offset

0,14

Comments

Number of compositions of n into parts p where 6 <= p <= 9. [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 (0,0,0,0,0,1,1,1,1).

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=1, a(7)=1, a(8)=1; for n>8, a(n) = a(n-6)+a(n-7)+a(n-8)+a(n-9). - Harvey P. Dale, Aug 18 2012

Mathematica

CoefficientList[Series[1/(1 - x^6 - x^7 - x^8 - x^9), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 1, 1, 1}, 60] (* Harvey P. Dale, Aug 18 2012 *)
CoefficientList[Series[1 / (1 - Total[x^Range[6, 9]]), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 27 2013 *)

Prog

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

Crossrefs

Sequence in context: A350862 A030340 A122453 * A134536 A214551 A343435

Adjacent sequences: A017846 A017847 A017848 * A017850 A017851 A017852

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved