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A356236
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Number of integer partitions of n with a neighborless part.
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10
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0, 1, 2, 2, 4, 4, 8, 9, 16, 20, 31, 40, 59, 76, 105, 138, 184, 238, 311, 400, 515, 656, 831, 1052, 1322, 1659, 2064, 2572, 3182, 3934, 4837, 5942, 7264, 8872, 10789, 13109, 15865, 19174, 23105, 27796, 33361, 39956, 47766, 56985, 67871, 80675, 95750, 113416
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OFFSET
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0,3
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COMMENTS
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A part x of a partition is neighborless if neither x - 1 nor x + 1 are parts.
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LINKS
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FORMULA
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EXAMPLE
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The a(1) = 1 through a(8) = 9 partitions:
(1) (2) (3) (4) (5) (6) (7)
(11) (111) (22) (41) (33) (52)
(31) (311) (42) (61)
(1111) (11111) (51) (331)
(222) (421)
(411) (511)
(3111) (4111)
(111111) (31111)
(1111111)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Function[ptn, Or@@Table[!MemberQ[ptn, x-1]&&!MemberQ[ptn, x+1], {x, Union[ptn]}]]]], {n, 0, 30}]
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CROSSREFS
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These partitions are ranked by the complement of A356736.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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