A227940 Number of runs of strictly increasing numbers of 2 X 2 squares in the list of partitions of n^2 into squares, where partition sorting order is ascending with larger squares taking higher precedence.

1, 1, 2, 3, 6, 12, 20, 42, 84, 171, 327, 654, 1288, 2533, 4942, 9566, 18481, 35449, 67649, 128372, 242451, 455393, 851352, 1583854, 2932250, 5403874, 9913868, 18107914, 32932025, 59643292

Offset: 1

Author

Christopher Hunt Gribble, Oct 03 2013

Keywords

• nonn

Examples

			For n = 4, the 8 partitions of 16 into square parts are:
Partition  Square side
.           1  2  3  4
.
.    1     16  0  0  0
.    2     12  1  0  0
.    3      8  2  0  0
.    4      4  3  0  0
.    5      0  4  0  0
.    6      7  0  1  0
.    7      3  1  1  0
.    8      0  0  0  1
So a(4) = 3 as there are 3 runs of 2 X 2 squares: (0,1,2,3,4) from partitions 1 to 5, (0,1) from partitions 6 to 7 and (0) from partition 8.
		

Links

• Christopher Hunt Gribble, C++ program

Crossrefs

Cf. A037444.