A368871 - OEIS

%I #6 Jan 15 2024 11:14:03

%S 1,1,1,1,1,1,1,1,1,19,28,41,60,88,129,189,277,406,595,872,1278,1873,

%T 2745,4023,5896,40893,64208,100816,158296,248548,390257,612761,962125,

%U 1510678,2371987,3724369,5847808,9181920,14416967,22636762,35543051

%N Number of compositions (ordered partitions) of n into odd parts not greater than sqrt(n).

%p b:= proc(n, t) option remember; `if`(n=0, 1, add(

%p      `if`(j::odd, b(n-j, t), 0), j=1..min(n, t)))

%p     end:

%p a:= n-> b(n, floor(sqrt(n))):

%p seq(a(n), n=0..40);  # _Alois P. Heinz_, Jan 13 2024

%t Table[SeriesCoefficient[1/(1 - Sum[Boole[OddQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 40}]

%Y Cf. A000045, A364526.

%K nonn

%O 0,10

%A _Ilya Gutkovskiy_, Jan 08 2024