A017864 Expansion of 1/(1-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15).

1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 4, 5, 6, 7, 9, 12, 14, 17, 21, 26, 32, 40, 51, 63, 77, 95, 117, 144, 178, 222, 276, 341, 422, 522, 645, 797, 987, 1223, 1513, 1872, 2317, 2867, 3547, 4390, 5435, 6726, 8322

Offset

0,15

Comments

Number of compositions of n into parts p where 7 <= p <= 15. [Joerg Arndt, Jun 28 2013]

Links

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

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

Formula

a(n) = a(n-7) +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>12. - Vincenzo Librandi, Jun 28 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[7, 15]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 28 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2}, 60] (* Harvey P. Dale, Sep 19 2022 *)

Prog

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^7-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, 1, 1, 1, 1, 1, 1, 1, 2 ]; [n le 15 select I[n] else Self(n-7)+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 28 2013

Crossrefs

Sequence in context: A281744 A026838 A182229 * A188937 A029035 A153178

Adjacent sequences: A017861 A017862 A017863 * A017865 A017866 A017867

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved