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A227103
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T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of two, with rows and columns of the latter in lexicographically nondecreasing order
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6
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2, 4, 4, 7, 15, 7, 11, 48, 48, 11, 16, 136, 239, 136, 16, 22, 341, 1084, 1084, 341, 22, 29, 771, 4444, 8427, 4444, 771, 29, 37, 1606, 16366, 60039, 60039, 16366, 1606, 37, 46, 3133, 54500, 384591, 754758, 384591, 54500, 3133, 46, 56, 5789, 166271, 2209056
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OFFSET
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1,1
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COMMENTS
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Table starts
..2....4......7.......11........16.........22.........29..........37.........46
..4...15.....48......136.......341........771.......1606........3133.......5789
..7...48....239.....1084......4444......16366......54500......166271.....470106
.11..136...1084.....8427.....60039.....384591....2209056....11456481...54141062
.16..341...4444....60039....754758....8638999...89104481...828893716.6983821643
.22..771..16366...384591...8638999..180409504.3428152304.58981679762
.29.1606..54500..2209056..89104481.3428152304
.37.3133.166271.11456481.828893716
.46.5789.470106.54141062
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..84
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FORMULA
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Empirical for column k:
k=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
k=2: [polynomial of degree 7] for n>3
k=3: [polynomial of degree 15] for n>5
k=4: [polynomial of degree 31] for n>13
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..0....0..1..0..0....0..1..0..0....0..0..0..1....0..0..0..1
..0..1..0..0....0..1..0..0....1..0..1..0....0..1..1..0....0..0..1..0
..1..0..1..0....0..0..0..0....1..1..1..0....1..1..1..0....0..0..0..0
..1..0..0..1....0..0..0..1....0..1..1..0....0..1..0..0....0..0..1..1
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CROSSREFS
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Column 1 is A000124
Sequence in context: A205744 A237859 A240338 * A223644 A223637 A223620
Adjacent sequences: A227100 A227101 A227102 * A227104 A227105 A227106
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin Jul 01 2013
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STATUS
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approved
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