

A234266


T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 2 (constant stress 1X1 tilings)


9



20, 46, 46, 104, 88, 104, 244, 170, 170, 244, 560, 358, 292, 358, 560, 1336, 754, 560, 560, 754, 1336, 3104, 1690, 1100, 988, 1100, 1690, 3104, 7504, 3746, 2324, 1816, 1816, 2324, 3746, 7504, 17600, 8722, 4924, 3616, 3188, 3616, 4924, 8722, 17600, 42976
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OFFSET

1,1


COMMENTS

Table starts
....20....46...104...244....560...1336...3104...7504...17600...42976..101504
....46....88...170...358....754...1690...3746...8722...19906...47458..110210
...104...170...292...560...1100...2324...4924..10988...24284...56060..127132
...244...358...560...988...1816...3616...7304..15544...33064...73288..161000
...560...754..1100..1816...3188...6076..11876..24340...50180..107044..227780
..1336..1690..2324..3616...6076..11140..21164..42076...84556..174700..361484
..3104..3746..4924..7304..11876..21164..39508..77060..152564..308756..627124
..7504..8722.10988.15544..24340..42076..77060.147892..289444..577732.1159268
.17600.19906.24284.33064..50180..84556.152564.289444..562580.1114036.2220884
.42976.47458.56060.73288.107044.174700.308756.577732.1114036.2191828.4349300
Empirical: also number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 6


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..541


FORMULA

Empirical for column k (k=2 recurrence also works for k=1; apparently all rows and columns have the same order 6 recurrence):
k=1: a(n) = 2*a(n1) +6*a(n2) 12*a(n3)
k=2..7: a(n) = 3*a(n1) +6*a(n2) 24*a(n3) +4*a(n4) +36*a(n5) 24*a(n6)


EXAMPLE

Some solutions for n=5 k=4
..0..2..0..2..0....0..2..2..2..0....2..2..1..2..1....0..2..0..2..0
..2..2..2..2..2....0..0..2..0..0....2..0..1..0..1....2..2..2..2..2
..2..0..2..0..2....0..2..2..2..0....1..1..0..1..0....2..0..2..0..2
..2..2..2..2..2....0..0..2..0..0....2..0..1..0..1....0..0..0..0..0
..0..2..0..2..0....2..0..0..0..2....1..1..0..1..0....0..2..0..2..0
..1..1..1..1..1....0..0..2..0..0....2..0..1..0..1....1..1..1..1..1


CROSSREFS

Sequence in context: A228319 A236474 A145220 * A234259 A135286 A338235
Adjacent sequences: A234263 A234264 A234265 * A234267 A234268 A234269


KEYWORD

nonn,tabl


AUTHOR

R. H. Hardin, Dec 22 2013


STATUS

approved



