A227940 - OEIS

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.

%I #13 Oct 05 2013 12:09:29

%S 1,1,2,3,6,12,20,42,84,171,327,654,1288,2533,4942,9566,18481,35449,

%T 67649,128372,242451,455393,851352,1583854,2932250,5403874,9913868,

%U 18107914,32932025,59643292

%N 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.

%H Christopher Hunt Gribble, <a href="/A227940/a227940.cpp.txt">C++ program</a>

%e For n = 4, the 8 partitions of 16 into square parts are:

%e Partition Square side

%e . 1 2 3 4

%e .

%e . 1 16 0 0 0

%e . 2 12 1 0 0

%e . 3 8 2 0 0

%e . 4 4 3 0 0

%e . 5 0 4 0 0

%e . 6 7 0 1 0

%e . 7 3 1 1 0

%e . 8 0 0 0 1

%e 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.

%Y Cf. A037444.

%K nonn

%O 1,3

%A _Christopher Hunt Gribble_, Oct 03 2013