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

Author

Paul D. Hanna, Aug 22 2005

Keywords

• nonn

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

Crossrefs

Cf. A111840, A078124 (variant).

Cf. A002449.

Programs

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]))}

Formula

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