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

%I #11 Oct 02 2020 16:42:57

%S 1,2,4,10,36,201,1625,17361,222241,3160641,47594625,738433281,

%T 11633144321,184687354881,2943499290625,47004182220801,

%U 751333186150401,12015464030289921,192200500444954625,3074832660977745921,49194319991205396481,787085099922532597761

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

%H Alois P. Heinz, <a href="/A210773/b210773.txt">Table of n, a(n) for n = 0..250</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (31,-310,1240,-1984,1024).

%F 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).

%F a(n) = [x^2^(n-1)] 1/(1-x) * 1/Product_{j=0..3} (1-x^(2^j)) for n>0.

%p 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);

%t LinearRecurrence[{31,-310,1240,-1984,1024},{1,2,4,10,36,201,1625,17361,222241},30] (* _Harvey P. Dale_, Oct 02 2020 *)

%Y Column k=4 of A152977.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Mar 26 2012