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A239883 Number of strict partitions of 2n + 1 having an ordering of the parts in which no two neighboring parts have the same parity.

%I A239883 #10 Apr 01 2014 04:19:26
%S A239883 1,2,3,5,7,10,13,18,23,31,41,55,73,99,132,177,236,313,412,540,701,904,
%T A239883 1159,1473,1861,2336,2915,3615,4463,5478,6698,8152,9887,11944,14391,
%U A239883 17280,20703,24739,29506,35115,41730,49501,58650,69389,82009,96807,114175
%N A239883 Number of strict partitions of 2n + 1 having an ordering of the parts in which no two neighboring parts have the same parity.
%C A239883 a(n) = number of strict partitions (that is, every part has multiplicity 1) of 2n + 1 having an ordering of the parts in which no two neighboring parts have the same parity.  This sequence is nondecreasing, unlike A239881, of which it is a bisection; the other bisection is A239882.
%H A239883 Alois P. Heinz, <a href="/A239883/b239883.txt">Table of n, a(n) for n = 0..500</a>
%e A239883 a(5) counts these 10 partitions of 11:  [11], [10,1], [9,2], [8,3], [8,1,2], [7,4], [6,5], [6,1,4], [6,3,2], [4,5,2].
%t A239883 d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; p[n_] := p[n] = Select[d[n], Abs[Count[#, _?OddQ] - Count[#, _?EvenQ]] <= 1 &]; t =  Table[p[n], {n, 0, 12}]
%t A239883 TableForm[t] (* shows the partitions *)
%t A239883 u = Table[Length[p[2 n + 1]], {n, 0, 20}]  (* A239883 *)
%t A239883 (* _Peter J. C. Moses_, Mar 10 2014 *)
%Y A239883 Cf. A239881, A239882, A239872.
%K A239883 nonn,easy
%O A239883 0,2
%A A239883 _Clark Kimberling_, Mar 29 2014
%E A239883 More terms from _Alois P. Heinz_, Mar 31 2014