A017858 - OEIS

A017858

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

1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 3, 6, 7, 6, 3, 1, 1, 4, 10, 16, 19, 16, 10, 5, 6, 15, 30, 45, 51, 45, 31, 21, 26, 51, 90, 126, 141, 127, 97, 78, 98, 167, 267, 357, 394, 365, 302, 273, 343, 532

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,16

COMMENTS

Number of compositions of n into parts 7, 8, and 9. [Joerg Arndt, Jun 28 2013]

LINKS

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

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

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; for n>8, a(n) = a(n-7)+a(n-8)+a(n-9). - Harvey P. Dale, Aug 17 2012

MATHEMATICA

CoefficientList[Series[1 / (1 - x^7 - x^8 - x^9), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 1}, 70] (* Harvey P. Dale, Aug 17 2012 *)

CoefficientList[Series[1 / (1 - Total[x^Range[7, 9]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 28 2013 *)

PROG

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^7-x^8-x^9))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 1, 1]; [n le 9 select I[n] else Self(n-7)+Self(n-8)+Self(n-9): n in [1..70]]; // Vincenzo Librandi, Jun 28 2013

CROSSREFS

Sequence in context: A334476 A319573 A178904 * A167769 A119369 A122445

Adjacent sequences: A017855 A017856 A017857 * A017859 A017860 A017861

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved