A017874 Expansion of 1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16).

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 16, 20, 25, 31, 38, 47, 56, 67, 80, 96, 116, 141, 172, 211, 257, 313, 380, 460, 556, 672, 813, 986, 1196, 1453, 1766, 2146, 2606, 3162

Offset

0,17

Comments

Number of compositions of n into parts p where 8 <= p <= 16. [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).

Formula

G.f.: 1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16).

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) for n>15. - Vincenzo Librandi, Jun 29 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[8, 16]]), {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, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1}, 60] (* Harvey P. Dale, Dec 05 2015 *)

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))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]; [n le 16 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): n in [1..70]]; // Vincenzo Librandi, Jun 29 2013

Crossrefs

Sequence in context: A033552 A062420 A089197 * A029016 A290807 A121385

Adjacent sequences: A017871 A017872 A017873 * A017875 A017876 A017877

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved