cp's OEIS Frontend

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 A227940 #13 Oct 05 2013 12:09:29
%S A227940 1,1,2,3,6,12,20,42,84,171,327,654,1288,2533,4942,9566,18481,35449,
%T A227940 67649,128372,242451,455393,851352,1583854,2932250,5403874,9913868,
%U A227940 18107914,32932025,59643292
%N 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.
%H A227940 Christopher Hunt Gribble, <a href="/A227940/a227940.cpp.txt">C++ program</a>
%e A227940 For n = 4, the 8 partitions of 16 into square parts are:
%e A227940 Partition  Square side
%e A227940 .           1  2  3  4
%e A227940 .
%e A227940 .    1     16  0  0  0
%e A227940 .    2     12  1  0  0
%e A227940 .    3      8  2  0  0
%e A227940 .    4      4  3  0  0
%e A227940 .    5      0  4  0  0
%e A227940 .    6      7  0  1  0
%e A227940 .    7      3  1  1  0
%e A227940 .    8      0  0  0  1
%e A227940 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 A227940 Cf. A037444.
%K A227940 nonn
%O A227940 1,3
%A A227940 _Christopher Hunt Gribble_, Oct 03 2013