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A239881 Number of strict partitions of n having an ordering in which no parts of equal parity are juxtaposed.

%I A239881 #9 Apr 02 2014 10:59:34
%S A239881 1,1,1,2,1,3,2,5,3,7,6,10,9,13,15,18,22,23,33,31,46,41,65,55,87,73,
%T A239881 117,99,153,132,199,177,254,236,324,313,408,412,512,540,639,701,795,
%U A239881 904,986,1159,1221,1473,1509,1861,1862,2336,2298,2915,2830,3615,3485
%N A239881 Number of strict partitions of n having an ordering in which no parts of equal parity are juxtaposed.
%C A239881 A strict partition is one in which every part has multiplicity 1.
%C A239881 a(n) = Sum_{k=-1..1} A240021(n,k). - _Alois P. Heinz_, Apr 02 2014
%H A239881 Alois P. Heinz, <a href="/A239881/b239881.txt">Table of n, a(n) for n = 0..1000</a>
%e A239881 a(12) counts these 9 partitions:  [12], [9,2,1], [3,8,1], [7,4,1], [7,2,3], [5,6,1], [6,3,2,1], [5,4,3], [5,4,1,2].
%t A239881 d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t A239881 p[n_] := p[n] = Select[d[n], Abs[Count[#, _?OddQ] - Count[#, _?EvenQ]] <= 1 &]; t =  Table[p[n], {n, 0, 12}]
%t A239881 TableForm[t] (* shows the partitions *)
%t A239881 u = Table[Length[p[n]], {n, 0, 60}]  (* A239880 *)
%t A239881 (* _Peter J. C. Moses_, Mar 10 2014 *)
%Y A239881 Cf. A239833, A239835, A239880.
%K A239881 nonn,easy
%O A239881 0,4
%A A239881 _Clark Kimberling_, Mar 29 2014