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).

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

Offset: 1

Author

David S. Newman, Aug 30 2018

Keywords

• nonn

Examples

			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).
		

References

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

Extensions

a(9)-a(61) from Robert Price, Sep 06 2018