cp's OEIS Frontend

A239832 Number of partitions of n having 1 more even part than odd, so that there is an ordering of parts for which the even and odd parts alternate and the first and last terms are even.

%I A239832 #11 Apr 01 2014 05:04:48
%S A239832 0,0,1,0,1,1,1,2,2,4,3,7,6,11,11,17,19,27,31,41,51,62,79,95,121,142,
%T A239832 182,212,269,314,393,459,570,665,816,958,1160,1364,1639,1928,2297,
%U A239832 2706,3200,3768,4434,5212,6105,7170,8361,9799,11396,13322,15450,18022
%N A239832 Number of partitions of n having 1 more even part than odd, so that there is an ordering of parts for which the even and odd parts alternate and the first and last terms are even.
%C A239832 Let c(n) be the number of partitions of n having 1 more odd part than even, so that there is an ordering of parts for which the even and odd parts alternate and the first and last terms are odd.  Then c(n) = a(n+1) for n >= 0.
%e A239832 The three partitions counted by a(10) are [10], [4,1,2,1,2], and [2,3,2,1,2].
%t A239832 p[n_] := p[n] = Select[IntegerPartitions[n], Count[#, _?OddQ] == -1 + Count[#, _?EvenQ] &]; t = Table[p[n], {n, 0, 10}]
%t A239832 TableForm[t] (* shows the partitions *)
%t A239832 Table[Length[p[n]], {n, 0, 30}]  (* A239832 *)
%t A239832 (* _Peter J. C. Moses_, Mar 10 2014 *)
%Y A239832 Cf. A239833, A239835, A045931, A239871.
%Y A239832 Column k=-1 of A240009.
%K A239832 nonn,easy
%O A239832 0,8
%A A239832 _Clark Kimberling_, Mar 29 2014