A017841 - OEIS

A017841

Expansion of 1/(1-x^5-x^6-x^7-x^8-x^9-x^10).

1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 7, 8, 10, 13, 17, 23, 29, 37, 47, 60, 78, 100, 129, 166, 213, 274, 351, 451, 580, 746, 960, 1233, 1584, 2035, 2615, 3362, 4321, 5554, 7138, 9173, 11789, 15150, 19471, 25025

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OFFSET

0,11

COMMENTS

Number of compositions of n into parts p where 5 <= p <= 10. [Joerg Arndt, Jun 27 2013]

LINKS

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

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

FORMULA

a(n) = a(n-5)+a(n-6)+a(n-7)+a(n-8)+a(n-9)+a(n-10), for n>9. - Vincenzo Librandi, Jun 27 2013

MATHEMATICA

CoefficientList[Series[1 / (1 - Total[x^Range[5, 10]]), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 27 2013 *)

LinearRecurrence[{0, 0, 0, 0, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 1, 1, 1, 1, 1}, 50] (* Robert G. Wilson v, Jun 27 2013 *)

PROG

(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^5-x^6-x^7-x^8-x^9-x^10))); /* or */ I:=[1, 0, 0, 0, 0, 1, 1, 1, 1, 1]; [n le 10 select I[n] else Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10): n in [1..70]]; // Vincenzo Librandi, Jun 27 2013

CROSSREFS

Sequence in context: A029012 A095699 A112192 * A304329 A111901 A316202

Adjacent sequences: A017838 A017839 A017840 * A017842 A017843 A017844

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved