A017824 Expansion of 1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11).

1, 0, 0, 1, 1, 1, 2, 3, 4, 6, 9, 13, 18, 27, 40, 57, 83, 122, 177, 257, 375, 546, 794, 1156, 1684, 2451, 3567, 5194, 7562, 11007, 16024, 23329, 33961, 49439, 71974, 104779, 152534, 222057, 323269, 470609, 685104

Offset

0,7

Comments

Number of compositions of n into parts p where 3 <= p <= 11. [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 (0,0,1,1,1,1,1,1,1,1,1).

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(10)=9; for n>10, 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) +a(n-11). - Harvey P. Dale, Sep 07 2012

Mathematica

CoefficientList[Series[1/(1 - Total[x^Range[3, 11]]), {x, 0, 40}], x] (* or *) LinearRecurrence[ {0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 1, 1, 1, 2, 3, 4, 6, 9}, 41] (* Harvey P. Dale, Sep 07 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-x^11))); /* or */ I:=[1, 0, 0, 1, 1, 1, 2, 3, 4, 6, 9]; [n le 11 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)+Self(n-11): n in [1..50]]; // Vincenzo Librandi, Jun 27 2013

Crossrefs

Sequence in context: A285484 A098889 A061481 * A343942 A094054 A001521

Adjacent sequences: A017821 A017822 A017823 * A017825 A017826 A017827

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved