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A318632
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Let a partition of n be written in binary. Join any two binary ones which are adjacent horizontally or vertically. If all the binary ones are connected count this partition in a(n).
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0
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1, 2, 2, 4, 3, 5, 5, 9, 8, 11, 12, 17, 16, 21, 24, 34, 34, 43, 47, 61, 65, 82, 92, 116, 124, 147, 166, 200, 220, 262, 293, 350, 383, 449, 504, 592, 654, 756, 846, 983, 1089, 1252, 1396, 1607, 1777, 2033, 2260, 2590, 2871, 3261, 3634, 4116, 4563, 5145, 5722, 6454, 7154, 8032, 8903, 9989, 11039
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OFFSET
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1,2
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REFERENCES
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George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976.
G. E. Andrews and K. Ericksson, Integer Partitions, Cambridge University Press 2004.
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LINKS
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EXAMPLE
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The partition of 7 = 3 + 2 + 2 looks like this in binary:
11
10
10
The binary ones are adjacent so this partition is counted in a(7).
The partition 7 = 5 + 2 looks like this in binary:
101
10
Since the binary ones are not adjacent horizontally or vertically this partition is not counted in a(7).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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