A210773 Number of partitions of 2^n into powers of 2 less than or equal to 16.

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

Alois P. Heinz, Table of n, a(n) for n = 0..250

Index entries for linear recurrences with constant coefficients, signature (31,-310,1240,-1984,1024).

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

Adjacent sequences: A210770 A210771 A210772 * A210774 A210775 A210776

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 26 2012

Status

approved