A092532 G.f.: 1/((1-x)*(1-x^4)*(1-x^8)).

1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 9, 9, 9, 9, 12, 12, 12, 12, 16, 16, 16, 16, 20, 20, 20, 20, 25, 25, 25, 25, 30, 30, 30, 30, 36, 36, 36, 36, 42, 42, 42, 42, 49, 49, 49, 49, 56, 56, 56, 56, 64, 64, 64, 64, 72, 72, 72, 72, 81, 81, 81, 81, 90, 90, 90, 90, 100, 100, 100, 100

Offset

0,5

Comments

Number of partitions of n into parts 1, 4, and 8. - Joerg Arndt, Aug 10 2014

Links

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

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Index entries for Molien series

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

Formula

a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=2, a(5)=2, a(6)=2, a(7)=2, a(8)=4, a(9)=4, a(10)=4, a(11)=4, a(12)=6; for n>12, a(n)=a(n-1)+a(n-4)-a(n-5)+a(n-8)- a(n-9)- a(n-12)+a (n-13). - Harvey P. Dale, Aug 10 2014

Mathematica

CoefficientList[Series[1/((1-x)(1-x^4)(1-x^8)), {x, 0, 80}], x] (* or *) LinearRecurrence[{1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, -1, 1}, {1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 4, 6}, 80] (* Harvey P. Dale, Aug 10 2014 *)

Prog

(Magma) [n le 13 select Floor(Floor(1+(n+3)/4)^2/4) else Self(n-1)+Self(n-4)-Self(n-5)+Self(n-8)-Self(n-9)-Self(n-12)+Self(n-13): n in [1..100]]; // Vincenzo Librandi, Aug 10 2014

Crossrefs

Sequence in context: A364932 A122461 A092533 * A073504 A092508 A032544

Adjacent sequences: A092529 A092530 A092531 * A092533 A092534 A092535

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 08 2004

Status

approved