A017850 Expansion of 1/(1-x^6-x^7-x^8-x^9-x^10).

1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 2, 3, 4, 5, 4, 4, 5, 7, 10, 15, 18, 20, 22, 25, 30, 41, 55, 70, 85, 100, 115, 138, 173, 221, 281, 351, 425, 508, 611, 747, 928, 1164, 1451, 1786, 2176, 2642, 3219, 3958, 4901, 6076

Offset

0,14

Comments

Number of compositions of n into parts p where 6 <= 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 (0,0,0,0,0,1,1,1,1,1).

Formula

a(n) = 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[6, 10]]), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 27 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 1, 1, 1, 1}, 60] (* Harvey P. Dale, Apr 28 2018 *)

Prog

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^6-x^7-x^8-x^9-x^10))); /* or */ I:=[1, 0, 0, 0, 0, 0, 1, 1, 1, 1]; [n le 10 select I[n] else 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: A368822 A270434 A204982 * A305901 A291520 A354445

Adjacent sequences: A017847 A017848 A017849 * A017851 A017852 A017853

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved