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.

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

Offset: 1

Author

R. H. Hardin Jan 06 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..144

Crossrefs

Column 1 is A189274(n+2)

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)