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A253159 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically 9
16, 39, 39, 69, 72, 69, 109, 88, 88, 109, 181, 120, 94, 120, 181, 325, 192, 129, 129, 192, 325, 613, 336, 201, 164, 201, 336, 613, 1189, 624, 345, 236, 236, 345, 624, 1189, 2341, 1200, 633, 380, 308, 380, 633, 1200, 2341, 4645, 2352, 1209, 668, 452, 452, 668, 1209 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...16...39...69..109..181..325..613.1189.2341.4645..9253.18469.36901.73765

...39...72...88..120..192..336..624.1200.2352.4656..9264.18480.36912.73776

...69...88...94..129..201..345..633.1209.2361.4665..9273.18489.36921.73785

..109..120..129..164..236..380..668.1244.2396.4700..9308.18524.36956.73820

..181..192..201..236..308..452..740.1316.2468.4772..9380.18596.37028.73892

..325..336..345..380..452..596..884.1460.2612.4916..9524.18740.37172.74036

..613..624..633..668..740..884.1172.1748.2900.5204..9812.19028.37460.74324

.1189.1200.1209.1244.1316.1460.1748.2324.3476.5780.10388.19604.38036.74900

.2341.2352.2361.2396.2468.2612.2900.3476.4628.6932.11540.20756.39188.76052

.4645.4656.4665.4700.4772.4916.5204.5780.6932.9236.13844.23060.41492.78356

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..1243

FORMULA

Empirical for rows, columns, diagonal: a(n) = 3*a(n-1) -2*a(n-2) for n>5

Empirical for max(n,k)>3: T(n,k) = 9*2^(n-1) + 9*2^(k-1) + c, where c=28 for min(n,k)=1, c=30 for min(n,k)=2, c=21 for min(n,k)=3, c=20 for min(n,k)>3

(no formula for the upper left 3X3 portion)

EXAMPLE

Some solutions for n=6 k=4

..1..1..1..1..1....0..0..0..0..0....0..1..1..1..1....0..0..0..0..0

..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0

..0..0..0..0..0....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0

..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0

..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....1..1..1..1..1

..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0

..1..1..1..1..1....0..0..0..0..1....1..1..1..1..1....1..1..1..1..1

CROSSREFS

Sequence in context: A218900 A070585 A253435 * A308311 A121375 A342976

Adjacent sequences:  A253156 A253157 A253158 * A253160 A253161 A253162

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 28 2014

STATUS

approved

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Last modified September 24 15:33 EDT 2021. Contains 347643 sequences. (Running on oeis4.)