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A227940
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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.
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2
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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
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OFFSET
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1,3
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LINKS
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EXAMPLE
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For n = 4, the 8 partitions of 16 into square parts are:
Partition Square side
. 1 2 3 4
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. 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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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