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A323583
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Number of ways to split an integer partition of n into consecutive subsequences.
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1
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1, 1, 3, 7, 17, 37, 83, 175, 373, 773, 1603, 3275, 6693, 13557, 27447, 55315, 111397, 223769, 449287, 900795, 1805465, 3615929, 7240327, 14491623, 29001625, 58027017, 116093259, 232237583, 464558201, 929224589, 1858623819, 3717475031, 7435314013, 14871103069
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..33.
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FORMULA
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a(n) = A070933(n)/2.
O.g.f.: (1/2)*Product_{n >= 1} 1/(1 - 2*x^n).
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EXAMPLE
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The a(3) = 7 ways to split an integer partition of 3 into consecutive subsequences are (3), (21), (2)(1), (111), (11)(1), (1)(11), (1)(1)(1).
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MATHEMATICA
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Table[Sum[2^(Length[ptn]-1), {ptn, IntegerPartitions[n]}], {n, 40}]
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CROSSREFS
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Cf. A006951, A070933, A100883, A279784, A279786, A323433, A323582.
Sequence in context: A026668 A111210 A033489 * A178941 A178155 A330457
Adjacent sequences: A323580 A323581 A323582 * A323584 A323585 A323586
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Jan 19 2019
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STATUS
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approved
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