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A210773
Number of partitions of 2^n into powers of 2 less than or equal to 16.
2
1, 2, 4, 10, 36, 201, 1625, 17361, 222241, 3160641, 47594625, 738433281, 11633144321, 184687354881, 2943499290625, 47004182220801, 751333186150401, 12015464030289921, 192200500444954625, 3074832660977745921, 49194319991205396481, 787085099922532597761
OFFSET
0,2
LINKS
FORMULA
G.f.: (256*x^8-400*x^7-42*x^6-169*x^5-470*x^4+734*x^3-252*x^2+29*x-1) / Product_{j=0..4} (2^j*x-1).
a(n) = [x^2^(n-1)] 1/(1-x) * 1/Product_{j=0..3} (1-x^(2^j)) for n>0.
MAPLE
a:= n-> `if`(n<4, [1, 2, 4, 10][n+1], (Matrix(5, (i, j)-> `if`(i=j-1, 1, `if`(i=5, [1024, -1984, 1240, -310, 31][j], 0)))^(n-4). <<36, 201, 1625, 17361, 222241>>)[1, 1]): seq(a(n), n=0..30);
MATHEMATICA
LinearRecurrence[{31, -310, 1240, -1984, 1024}, {1, 2, 4, 10, 36, 201, 1625, 17361, 222241}, 30] (* Harvey P. Dale, Oct 02 2020 *)
CROSSREFS
Column k=4 of A152977.
Sequence in context: A243567 A323949 A066278 * A210774 A210775 A210776
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Mar 26 2012
STATUS
approved