A017823 Expansion of 1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10).

1, 0, 0, 1, 1, 1, 2, 3, 4, 6, 9, 12, 18, 27, 38, 55, 81, 117, 169, 246, 357, 517, 751, 1090, 1580, 2293, 3328, 4827, 7003, 10162, 14743, 21389, 31034, 45026, 65325, 94779, 137512, 199509, 289461, 419970, 609317

Offset

0,7

Comments

Number of compositions of n into parts p where 3 <= p <= 10. - 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 (0,0,1,1,1,1,1,1,1,1).

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=1, a(5)=1, a(6)=2, a(7)=3, a(8)=4, a(9)=6, a(n)=a(n-3)+a(n-4)+a(n-5)+a(n-6)+a(n-7)+a(n-8)+a(n-9)+a(n-10). - Harvey P. Dale, Feb 14 2012

Mathematica

CoefficientList[Series[1/(1+Total[-x^Range[3, 10]]), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 0, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 1, 1, 1, 2, 3, 4, 6}, 41] (* Harvey P. Dale, Feb 14 2012 *)

Prog

(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10))); /* or */ I:=[1, 0, 0, 1, 1, 1, 2, 3, 4, 6]; [n le 10 select I[n] else Self(n-3)+Self(n-4)+Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10): n in [1..50]]; // Vincenzo Librandi, Jun 27 2013

Crossrefs

Sequence in context: A018393 A018287 A199014 * A017982 A139076 A126011

Adjacent sequences: A017820 A017821 A017822 * A017824 A017825 A017826

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved