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%I #21 Mar 05 2020 10:09:35
%S 0,1,1,1,1,1,1,1,1,2,2,3,4,5,6,8,9,11,13,15,17,20,22,25,28,32,35,40,
%T 44,50,56,63,70,80,89,101,113,128,143,162,181,204,228,256,285,320,355,
%U 396,439,489,540,599,660,730,803,886,972,1070,1172,1287,1408,1544,1686,1846,2014,2202,2400,2621,2854,3114,3389,3693,4016,4374,4753,5172,5617,6107,6628,7201,7810
%N Number of partitions of n with parts differing by at least two and with an odd number of parts.
%H Alois P. Heinz, <a href="/A286316/b286316.txt">Table of n, a(n) for n = 0..5000</a>
%F a(n) = A003114(n) - A286041(n).
%F a(n) ~ phi^(1/2) * exp(2*Pi*sqrt(n/15)) / (4 * 3^(1/4) * 5^(1/2) * n^(3/4)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Mar 05 2020
%t Table[Length@
%t Select[IntegerPartitions@n, Min[-Differences@#] > 1 && OddQ@Length@# &], {n, 80}]
%Y Cf. A003114, A286041, A039924.
%K nonn
%O 0,10
%A _George Beck_, May 06 2017
%E a(0)=0 prepended by _Alois P. Heinz_, May 07 2017
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