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 A203835 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements 8
 45, 225, 225, 1125, 1971, 1125, 5625, 17289, 17289, 5625, 28125, 151659, 270333, 151659, 28125, 140625, 1330353, 4238721, 4238721, 1330353, 140625, 703125, 11669859, 66490965, 119606211, 66490965, 11669859, 703125, 3515625, 102368025 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ......45.......225.........1125...........5625.............28125 .....225......1971........17289.........151659...........1330353 ....1125.....17289.......270333........4238721..........66490965 ....5625....151659......4238721......119606211........3383285769 ...28125...1330353.....66490965.....3383285769......173185290765 ..140625..11669859...1043088057....95763046491.....8882824128417 ..703125.102368025..16363800045..2710984443345...455911325162757 .3515625.897972507.256713156657.76749227497395.23404859123410809 LINKS R. H. Hardin, Table of n, a(n) for n = 1..144 FORMULA Empirical for column k: k=1: a(n) = 9*5^n k=2: a(n) = 9*a(n-1) -2*a(n-2) k=3: a(n) = 19*a(n-1) -54*a(n-2) +32*a(n-3) k=4: a(n) = 31*a(n-1) -24*a(n-2) -1612*a(n-3) +3816*a(n-4) +1152*a(n-5) -2784*a(n-6) +256*a(n-7) k=5: (order 12 recurrence) k=6: (order 28 recurrence) k=7: (order 54 recurrence) EXAMPLE Some solutions for n=4 k=3 ..0..2..0..1....2..1..0..0....0..1..2..0....0..0..2..0....2..1..0..2 ..2..0..1..0....1..1..1..0....1..2..2..2....0..2..2..2....2..2..1..0 ..0..2..0..1....2..1..2..1....0..1..2..2....1..0..2..2....1..2..2..1 ..2..0..0..0....2..2..2..2....0..0..1..2....2..1..0..2....0..1..2..2 ..2..2..0..1....1..2..1..2....2..0..0..1....1..2..1..0....2..0..1..2 CROSSREFS Column 1 is A189274(n+2) Sequence in context: A091197 A184539 A146302 * A087442 A280059 A251451 Adjacent sequences:  A203832 A203833 A203834 * A203836 A203837 A203838 KEYWORD nonn,tabl AUTHOR R. H. Hardin Jan 06 2012 STATUS approved

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