cp's OEIS Frontend

A300788 Number of strict integer partitions of n in which the even parts appear as often at even positions as at odd positions.

%I A300788 #18 Jan 04 2021 18:49:16
%S A300788 1,1,0,1,1,1,2,2,3,3,4,5,6,7,8,10,12,14,16,19,23,26,30,35,42,47,54,62,
%T A300788 73,82,94,107,124,139,158,179,206,230,260,293,334,372,420,470,532,591,
%U A300788 664,740,835,924,1034,1148,1288,1422,1588,1756,1962,2161,2404
%N A300788 Number of strict integer partitions of n in which the even parts appear as often at even positions as at odd positions.
%H A300788 Alois P. Heinz, <a href="/A300788/b300788.txt">Table of n, a(n) for n = 0..4000</a> (first 291 terms from Fausto A. C. Cariboni)
%e A300788 The a(9) = 3 strict partitions: (9), (621), (531). Missing are: (81), (72), (63), (54), (432).
%t A300788 cobal[y_]:=Sum[(-1)^x,{x,Join@@Position[y,_?EvenQ]}];
%t A300788 Table[Length[Select[IntegerPartitions[n],cobal[#]===0&&UnsameQ@@#&]],{n,0,40}]
%Y A300788 Cf. A000712, A000898, A001405, A026010, A045931, A063886, A097613, A130780, A171966, A239241, A300787, A300789.
%K A300788 nonn
%O A300788 0,7
%A A300788 _Gus Wiseman_, Mar 12 2018
%E A300788 a(41)-a(58) from _Alois P. Heinz_, Mar 13 2018