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A350846
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Number of integer partitions of n with at least two adjacent parts of quotient 2.
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6
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0, 0, 0, 1, 1, 2, 4, 5, 8, 12, 18, 25, 36, 48, 65, 89, 119, 157, 207, 269, 350, 448, 574, 729, 927, 1166, 1465, 1830, 2282, 2827, 3501, 4309, 5300, 6483, 7923, 9641, 11718, 14187, 17155, 20674, 24885, 29860, 35787, 42772, 51054, 60791, 72289, 85772, 101641
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OFFSET
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0,6
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LINKS
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EXAMPLE
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The a(3) = 1 through a(9) = 12 partitions:
(21) (211) (221) (42) (421) (422) (63)
(2111) (321) (2221) (521) (621)
(2211) (3211) (3221) (3321)
(21111) (22111) (4211) (4221)
(211111) (22211) (5211)
(32111) (22221)
(221111) (32211)
(2111111) (42111)
(222111)
(321111)
(2211111)
(21111111)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], MemberQ[Divide@@@Partition[#, 2, 1], 2]&]], {n, 0, 30}]
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CROSSREFS
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Cf. A000929, A003000, A003114, A018819, A045690, A045691, A116931, A120641, A154402, A323093, A342094, A342095, A342096, A342098.
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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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