A017869 Expansion of 1/(1-x^8-x^9-x^10-x^11).

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 3, 6, 10, 12, 12, 10, 6, 4, 5, 10, 20, 31, 40, 44, 40, 32, 25, 25, 39, 66, 101, 135, 155, 156, 141, 122, 121, 155, 231, 341, 457, 547, 587, 574, 540

Offset

0,18

Comments

Number of compositions of n into parts p where 8 <= p <= 11. [Joerg Arndt, Jun 29 2013]

Links

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

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

Formula

G.f.: 1/(1-x^8-x^9-x^10-x^11).

a(n) = a(n-8) +a(n-9) +a(n-10) +a(n-11) for n>10. - Vincenzo Librandi, Jun 29 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[8, 11]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 29 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1}, 60] (* Harvey P. Dale, Dec 31 2018 *)

Prog

(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9-x^10-x^11))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]; [n le 11 select I[n] else Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11): n in [1..70]]; // Vincenzo Librandi, Jun 29 2013

Crossrefs

Sequence in context: A017879 A179764 A266313 * A107469 A167600 A008287

Adjacent sequences: A017866 A017867 A017868 * A017870 A017871 A017872

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved