A017873 - OEIS

A017873

Expansion of 1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15).

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 8, 9, 11, 14, 18, 23, 29, 36, 43, 50, 58, 68, 81, 98, 120, 148, 183, 224, 271, 325, 388, 463, 554, 666, 806, 980, 1193, 1450, 1757, 2122, 2556, 3074

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OFFSET

0,18

COMMENTS

Number of compositions of n into parts p where 8 <= p <= 15. [Joerg Arndt, Jun 29 2013]

LINKS

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

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

FORMULA

a(n) = a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) for n>14. - Vincenzo Librandi, Jun 29 2013

MATHEMATICA

CoefficientList[Series[1 / (1 - Total[x^Range[8, 15]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 29 2013 *)

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1}, 60] (* Harvey P. Dale, Dec 04 2019 *)

PROG

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]; [n le 15 select I[n] else Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15): n in [1..70]]; // Vincenzo Librandi, Jun 29 2013

CROSSREFS

Sequence in context: A252373 A245338 A160755 * A274016 A291572 A265541

Adjacent sequences: A017870 A017871 A017872 * A017874 A017875 A017876

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved