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A239881
Number of strict partitions of n having an ordering in which no parts of equal parity are juxtaposed.
5
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, 117, 99, 153, 132, 199, 177, 254, 236, 324, 313, 408, 412, 512, 540, 639, 701, 795, 904, 986, 1159, 1221, 1473, 1509, 1861, 1862, 2336, 2298, 2915, 2830, 3615, 3485
OFFSET
0,4
COMMENTS
A strict partition is one in which every part has multiplicity 1.
a(n) = Sum_{k=-1..1} A240021(n,k). - Alois P. Heinz, Apr 02 2014
LINKS
EXAMPLE
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].
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[n]], {n, 0, 60}] (* A239880 *)
(* Peter J. C. Moses, Mar 10 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 29 2014
STATUS
approved