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A350837
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Number of integer partitions of n with no adjacent parts of quotient 2.
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11
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1, 1, 2, 2, 4, 5, 7, 10, 14, 18, 24, 31, 41, 53, 70, 87, 112, 140, 178, 221, 277, 344, 428, 526, 648, 792, 971, 1180, 1436, 1738, 2103, 2533, 3049, 3660, 4387, 5242, 6259, 7450, 8860, 10511, 12453, 14723, 17387, 20489, 24121, 28343, 33269, 38982, 45632, 53327
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OFFSET
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0,3
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COMMENTS
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The first of these partitions that is not double-free (see A323092 for definition) is (4,3,2).
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LINKS
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EXAMPLE
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The a(1) = 1 through a(7) = 10 partitions:
(1) (2) (3) (4) (5) (6) (7)
(11) (111) (22) (32) (33) (43)
(31) (41) (51) (52)
(1111) (311) (222) (61)
(11111) (411) (322)
(3111) (331)
(111111) (511)
(4111)
(31111)
(1111111)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], FreeQ[Divide@@@Partition[#, 2, 1], 2]&]], {n, 0, 15}]
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CROSSREFS
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The sets version (subsets of prescribed maximum) is A045691.
These partitions are ranked by A350838.
Cf. A000070, A003000, A003114, `A003242, A051424, `A101417, A120641, A154402, A305148, A323093, A323094, A342095, A350839.
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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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