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A369222 Number of compositions (ordered partitions) of n into powers of 2 not greater than sqrt(n).

%I A369222 #13 Jan 22 2024 18:20:10
%S A369222 1,1,1,1,5,8,13,21,34,55,89,144,233,377,610,987,4930,8651,15182,26642,
%T A369222 46754,82047,143983,252672,443409,778128,1365520,2396320,4205249,
%U A369222 7379697,12950466,22726483,39882198,69988378,122821042,215535903,378239143,663763424
%N A369222 Number of compositions (ordered partitions) of n into powers of 2 not greater than sqrt(n).
%H A369222 Alois P. Heinz, <a href="/A369222/b369222.txt">Table of n, a(n) for n = 0..4048</a>
%p A369222 b:= proc(n, t) option remember; `if`(n=0, 1,
%p A369222       add(b(n-2^j, t), j=0..min(ilog2(n), t)))
%p A369222     end:
%p A369222 a:= n-> b(n, ilog2(floor(sqrt(n)))):
%p A369222 seq(a(n), n=0..37);  # _Alois P. Heinz_, Jan 18 2024
%t A369222 Table[SeriesCoefficient[1/(1 - Sum[Boole[IntegerQ[Log[2, k]]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 37}]
%Y A369222 Cf. A000045, A023359, A109696, A364526.
%K A369222 nonn
%O A369222 0,5
%A A369222 _Ilya Gutkovskiy_, Jan 16 2024