|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
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.
|
|
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
|
|
|
|