A017870 - OEIS

A017870

Expansion of 1/(1-x^8-x^9-x^10-x^11-x^12).

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 2, 3, 6, 10, 15, 18, 19, 18, 16, 14, 16, 23, 36, 52, 68, 80, 86, 85, 83, 87, 105, 141, 195, 259, 322, 371, 402, 421, 446, 501, 611, 787, 1022, 1288

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OFFSET

0,18

COMMENTS

Number of compositions of n into parts p where 8 <= p <= 12. [Joerg Arndt, Jun 29 2013]

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) for n>11. - Vincenzo Librandi, Jun 29 2013

MATHEMATICA

CoefficientList[Series[1 / (1 - Total[x^Range[8, 12]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 29 2013 *)

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1}, 60] (* Harvey P. Dale, Dec 31 2023 *)

PROG

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9-x^10-x^11-x^12))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1]; [n le 12 select I[n] else Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12): n in [1..70]]; // Vincenzo Librandi, Jun 29 2013

CROSSREFS

Sequence in context: A062406 A271800 A073792 * A017860 A328765 A368822

Adjacent sequences: A017867 A017868 A017869 * A017871 A017872 A017873

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved