A017875 Expansion of 1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17).

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 10, 13, 15, 18, 22, 27, 33, 40, 49, 61, 74, 89, 108, 131, 159, 193, 235, 288, 352, 428, 521, 634, 771, 937, 1139, 1387, 1690, 2057, 2504, 3049

Offset

0,17

Comments

Number of compositions of n into parts p where 8 <= p <= 17. [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 (0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1).

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) +a(n-16) +a(n-17) for n>16. - Vincenzo Librandi, Jun 29 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[8, 17]]), {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, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2}, 60] (* Harvey P. Dale, Oct 13 2013 *)

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-x^16-x^17))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2]; [n le 17 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)+Self(n-16)+Self(n-17): n in [1..70]]; // Vincenzo Librandi, Jun 29 2013

Crossrefs

Sequence in context: A011877 A029064 A029037 * A039732 A011876 A029036

Adjacent sequences: A017872 A017873 A017874 * A017876 A017877 A017878

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved