A017840 Expansion of 1/(1-x^5-x^6-x^7-x^8-x^9).

1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 5, 6, 8, 11, 15, 19, 23, 28, 35, 45, 59, 76, 96, 120, 150, 190, 243, 311, 396, 501, 632, 799, 1014, 1290, 1641, 2083, 2639, 3342, 4236, 5376, 6827, 8667, 10995, 13941, 17676

Offset

0,12

Comments

Number of compositions of n into parts p where 5 <= 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 (0,0,0,0,1,1,1,1,1).

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=1, a(6)=1, a(7)=1, a(8)=1; for n>8, a(n) = a(n-5)+a(n-6)+a(n-7)+a(n-8)+a(n-9). [Harvey P. Dale, Sep 24 2011]

Mathematica

CoefficientList[Series[1/(1-x^5-x^6-x^7-x^8-x^9), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 1, 1, 1, 1}, 50] (* Harvey P. Dale, Sep 24 2011 *)
CoefficientList[Series[1 / (1 - Total[x^Range[5, 9]]), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 27 2013 *)

Prog

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^5-x^6-x^7-x^8-x^9))); /* or */ I:=[1, 0, 0, 0, 0, 1, 1, 1, 1]; [n le 9 select I[n] else Self(n-5)+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: A330292 A017866 A086886 * A017855 A051598 A086993

Adjacent sequences: A017837 A017838 A017839 * A017841 A017842 A017843

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved