A111841 Number of partitions of 3^n-1 into powers of 3, also equals column 0 of triangle A111840, which shifts columns left and up under matrix cube.

1, 1, 3, 18, 216, 5589, 336555, 49768101, 18707873562, 18299531019402, 47379925800261099, 328983441917303863134, 6190598463101580564238419, 318441251661562459898972204796, 45106336219710244780433937129788943

Offset

0,3

Comments

Let q=3; a(n) equals the partitions of q^n-1 into powers of q, or, the coefficient of x^(q^n-1) in 1/Product_{j>=0}(1-x^(q^j)).

Links

T. D. Noe, Table of n, a(n) for n=0..40

Formula

a(n) = [x^(3^n-1)] Product_{k>=0} 1/(1-x^(3^k)).

Prog

(PARI) {a(n, q=3)=local(A=Mat(1), B); if(n<0, 0, for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, if(j==1, B[i, j]=(A^q)[i-1, 1], B[i, j]=(A^q)[i-1, j-1])); )); A=B); return(A[n+1, 1]))}

Crossrefs

Cf. A111840, A078124 (variant).

Cf. A002449.

Sequence in context: A163883 A319580 A132727 * A279233 A071605 A340336

Adjacent sequences: A111838 A111839 A111840 * A111842 A111843 A111844

Keyword

nonn

Author

Paul D. Hanna, Aug 22 2005

Status

approved