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A017879 Expansion of 1/(1-x^9-x^10-x^11-x^12). 1
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 1, 3, 6, 10, 12, 12, 10, 6, 3, 2, 4, 10, 20, 31, 40, 44, 40, 31, 21, 15, 19, 36, 65, 101, 135, 155, 155, 136, 107, 86, 91, 135, 221, 337, 456, 546 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,20

COMMENTS

Number of compositions (ordered partitions) of n into parts 9, 10, 11 and 12. - Ilya Gutkovskiy, May 27 2017

LINKS

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

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

FORMULA

a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=0, a(8)=0, a(9)=1, a(10)=1, a(11)=1; for n>11, a(n) = a(n-9)+a(n-10)+a(n-11)+a(n-12). - Harvey P. Dale, Apr 29 2013

MATHEMATICA

CoefficientList[Series[1 / (1 - x^9 - x^10 - x^11 - x^12), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1}, 70] (* Harvey P. Dale, Apr 29 2013 *)

CoefficientList[Series[1 / (1 - Total[x^Range[9, 12]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jul 01 2013 *)

PROG

(MAGMA) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^9-x^10-x^11-x^12))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]; [n le 12 select I[n] else Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12): n in [1..70]]; // Vincenzo Librandi, Jul 01 2013

CROSSREFS

Sequence in context: A141470 A141331 A017889 * A179764 A266313 A017869

Adjacent sequences:  A017876 A017877 A017878 * A017880 A017881 A017882

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified May 16 01:55 EDT 2021. Contains 343937 sequences. (Running on oeis4.)