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A239882
Number of strict partitions of 2n having an ordering of the parts in which no two neighboring parts have the same parity.
2
1, 1, 1, 2, 3, 6, 9, 15, 22, 33, 46, 65, 87, 117, 153, 199, 254, 324, 408, 512, 639, 795, 986, 1221, 1509, 1862, 2298, 2830, 3485, 4285, 5267, 6460, 7920, 9687, 11836, 14426, 17557, 21310, 25823, 31204, 37632, 45262, 54326, 65029, 77678, 92549, 110035, 130509
OFFSET
0,4
COMMENTS
a(n) = number of strict partitions (that is, every part has multiplicity 1) of 2n 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 A239883.
LINKS
EXAMPLE
a(6) counts these 9 partitions of 12: [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]
MATHEMATICA
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}]
TableForm[t] (* shows the partitions *)
u = Table[Length[p[2 n]], {n, 0, 40}] (* A239882 *)
(* Peter J. C. Moses, Mar 10 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 29 2014
EXTENSIONS
More terms from Alois P. Heinz, Mar 31 2014
STATUS
approved