

A318632


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).


0



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

1,2


REFERENCES

George E. Andrews, The Theory of Partitions, AddisonWesley, Reading, Mass., 1976.
G. E. Andrews and K. Ericksson, Integer Partitions, Cambridge University Press 2004.


LINKS



EXAMPLE

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).


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



