

A239883


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


2



1, 2, 3, 5, 7, 10, 13, 18, 23, 31, 41, 55, 73, 99, 132, 177, 236, 313, 412, 540, 701, 904, 1159, 1473, 1861, 2336, 2915, 3615, 4463, 5478, 6698, 8152, 9887, 11944, 14391, 17280, 20703, 24739, 29506, 35115, 41730, 49501, 58650, 69389, 82009, 96807, 114175
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OFFSET

0,2


COMMENTS

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.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500


EXAMPLE

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].


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 + 1]], {n, 0, 20}] (* A239883 *)
(* Peter J. C. Moses, Mar 10 2014 *)


CROSSREFS

Cf. A239881, A239882, A239872.
Sequence in context: A008628 A038499 A118199 * A088318 A038083 A238863
Adjacent sequences: A239880 A239881 A239882 * A239884 A239885 A239886


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Mar 29 2014


EXTENSIONS

More terms from Alois P. Heinz, Mar 31 2014


STATUS

approved



