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A368868 Number of partitions of n into odd parts not greater than sqrt(n).

%I A368868 #9 Jan 16 2024 16:47:37
%S A368868 1,1,1,1,1,1,1,1,1,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,29,31,33,35,37,40,
%T A368868 42,44,47,49,52,55,57,60,63,66,69,72,75,78,82,85,88,92,292,308,324,
%U A368868 341,358,376,395,414,434,454,475,497,519,542,566,590,615,641,667,694,722,751
%N A368868 Number of partitions of n into odd parts not greater than sqrt(n).
%H A368868 Alois P. Heinz, <a href="/A368868/b368868.txt">Table of n, a(n) for n = 0..10000</a>
%p A368868 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A368868       b(n, i-1)+`if`(i::odd, b(n-i, min(n-i, i)), 0)))
%p A368868     end:
%p A368868 a:= n-> b(n, floor(sqrt(n))):
%p A368868 seq(a(n), n=0..70);  # _Alois P. Heinz_, Jan 13 2024
%t A368868 Table[SeriesCoefficient[Product[1/(1 - Boole[OddQ[k]] x^k), {k, 1, Floor[Sqrt[n]]}], {x, 0, n}], {n, 0, 70}]
%Y A368868 Cf. A000009, A097356.
%K A368868 nonn
%O A368868 0,10
%A A368868 _Ilya Gutkovskiy_, Jan 08 2024