A017862 Expansion of 1/(1-x^7-x^8-x^9-x^10-x^11-x^12-x^13).

1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 7, 8, 10, 13, 17, 22, 28, 34, 40, 47, 56, 68, 84, 105, 132, 164, 201, 244, 295, 357, 434, 532, 656, 810, 998, 1225, 1498, 1827, 2227, 2719, 3328, 4082, 5012

Offset

0,16

Comments

Number of compositions of n into parts p where 7 <= p <= 13. [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).

Formula

a(n) = a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) for n>12. - Vincenzo Librandi, Jun 28 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[7, 13]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 28 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1}, 60] (* Harvey P. Dale, Feb 25 2018 *)

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))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ]; [n le 13 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): n in [1..70]]; // Vincenzo Librandi, Jun 28 2013

Crossrefs

Sequence in context: A238401 A337978 A332713 * A265539 A254926 A155919

Adjacent sequences: A017859 A017860 A017861 * A017863 A017864 A017865

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved