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Column 1 is A005010(n-1)A253307

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R. H. Hardin, <a href="/A253662/b253662.txt">Table of n, a(n) for n = 1..144</a>

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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock diagonal maximum minus antidiagonal maximum unequal to its neighbors horizontally, vertically and nw-se diagonally

81, 518, 518, 3550, 3318, 3550, 23524, 25062, 25062, 23524, 157476, 181308, 241548, 181308, 157476, 1051870, 1284808, 2113406, 2113406, 1284808, 1051870, 7027770, 9172142, 17719343, 21509980, 17719343, 9172142, 7027770, 46953514, 65613880

1,1

Table starts

.........81.........518.........3550..........23524..........157476

........518........3318........25062.........181308.........1284808

.......3550.......25062.......241548........2113406........17719343

......23524......181308......2113406.......21509980.......213776286

.....157476.....1284808.....17719343......213776286......2673402320

....1051870.....9172142....152352910.....2149355346.....32368598122

....7027770....65613880...1302707432....21597168872....395496194486

...46953514...467877898..11094507660...212331840928...4770936979106

..313711862..3342085566..94827318012..2118953225888..57860771981049

.2095963398.23863144636.808751503976.21018774727072.697085769177592

Empirical for column k:

k=1: [linear recurrence of order 10] for n>11

k=2: [order 76] for n>80

Some solutions for n=2 k=4

..0..1..0..0..0....2..0..2..0..2....0..1..2..0..1....1..1..0..1..0

..0..0..0..2..0....2..0..0..2..1....1..2..0..0..2....1..0..2..1..2

..0..0..2..1..2....1..0..2..1..0....2..0..2..2..0....2..1..0..2..2

Column 1 is A005010(n-1)

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nonn,tabl

R. H. Hardin, Jan 07 2015

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