login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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

%I #25 Sep 06 2018 19:23:38

%S 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,

%T 147,166,200,220,262,293,350,383,449,504,592,654,756,846,983,1089,

%U 1252,1396,1607,1777,2033,2260,2590,2871,3261,3634,4116,4563,5145,5722,6454,7154,8032,8903,9989,11039

%N 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).

%D George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976.

%D G. E. Andrews and K. Ericksson, Integer Partitions, Cambridge University Press 2004.

%e The partition of 7 = 3 + 2 + 2 looks like this in binary:

%e 11

%e 10

%e 10

%e The binary ones are adjacent so this partition is counted in a(7).

%e The partition 7 = 5 + 2 looks like this in binary:

%e 101

%e 10

%e Since the binary ones are not adjacent horizontally or vertically this partition is not counted in a(7).

%K nonn

%O 1,2

%A _David S. Newman_, Aug 30 2018

%E a(9)-a(61) from _Robert Price_, Sep 06 2018