A017859 Expansion of 1/(1-x^7-x^8-x^9-x^10).

1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 2, 3, 4, 3, 2, 1, 1, 3, 6, 10, 12, 12, 10, 7, 7, 11, 20, 31, 40, 44, 41, 36, 35, 45, 69, 102, 135, 156, 161, 156, 157, 185, 251, 351, 462, 554, 608, 630, 659, 749, 944, 1249, 1618

Offset

0,16

Comments

Number of compositions of n into parts p where 7 <= p <= 10. [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).

Formula

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

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[7, 10]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 28 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 1}, 60] (* Harvey P. Dale, Jun 21 2022 *)

Prog

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^7-x^8-x^9-x^10))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 1, 1, 1]; [n le 10 select I[n] else Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10): n in [1..70]]; // Vincenzo Librandi, Jun 28 2013

Crossrefs

Sequence in context: A107469 A167600 A008287 * A171456 A028356 A232244

Adjacent sequences: A017856 A017857 A017858 * A017860 A017861 A017862

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved