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

Author

Alois P. Heinz, Mar 26 2012

Keywords

• nonn
• easy

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).

Crossrefs

Column k=4 of A152977.

Programs

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 *)

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.