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A078537
Number of partitions of 4^n into powers of 4 (without regard to order).
11
1, 2, 6, 46, 1086, 79326, 18583582, 14481808030, 38559135542174, 357934565638890910, 11766678027350761752990, 1387043469046575118555443614, 592264246356176268834689653440926, 923812464024548700407122072128655860126, 5301247577915139769925461060755690116740047262
OFFSET
0,2
COMMENTS
Conjecture: a(n) = sum of the n-th row of lower triangular matrix A078536.
LINKS
FORMULA
a(n) = coefficient of x^(4^n) in power series expansion of 1/[(1-x)(1-x^4)(1-x^16)...(1-x^(4^k))...].
EXAMPLE
a(2) = 6 since partitions of 4^2 into powers of 4 are: [16], [4,4,4,4], [4,4,4,1,1,1,1], [4,4,1,1,1,1,1,1,1,1], [4,1,1,1,1,1,1,1,1,1,1,1,1], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1].
MATHEMATICA
a[0] = 1; a[n_] := a[n] = a[n - 1] + a[Floor[n/4]]; b = Table[ a[n], {n, 0, 4^9}]; Table[ b[[4^n + 1]], {n, 0, 9}]
CROSSREFS
Column k=4 of A145515.
Sequence in context: A316073 A001587 A306784 * A145502 A274702 A072444
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 29 2002
EXTENSIONS
Extended by Robert G. Wilson v, Dec 01 2002
More terms from Alois P. Heinz, Oct 11 2008
STATUS
approved