A111817 Number of partitions of 3*4^n into powers of 4, also equals column 1 of triangle A078536, which shifts columns left and up under matrix 4th power.

1, 4, 28, 524, 29804, 5423660, 3276048300, 6744720496300, 48290009081437356, 1221415413140406958252, 110523986015743458745929900, 36150734459755630877180158951596

Offset

0,2

Comments

Let q=4; a(n) equals the partitions of (q-1)*q^n into powers of q, or, the coefficient of x^((q-1)*q^n) in 1/Product_{j>=0}(1-x^(q^j)).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..40

Formula

a(n) = [x^(3*4^n)] 1/Product_{j>=0}(1-x^(4^j)).

Prog

(PARI) a(n, q=4)=local(A=Mat(1), B); if(n<0, 0, for(m=1, n+2, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i || j==1, B[i, j]=1, B[i, j]=(A^q)[i-1, j-1]); )); A=B); return(A[n+2, 2]))

Crossrefs

Cf. A078536 (triangle), A002577 (q=2), A078124 (q=3), A111821 (q=5), A111826 (q=6), A111831 (q=7), A111836 (q=8).

Sequence in context: A197872 A203220 A338816 * A134048 A091969 A101346

Adjacent sequences: A111814 A111815 A111816 * A111818 A111819 A111820

Keyword

nonn

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Status

approved