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

1,1

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 A334035 A280059

Adjacent sequences: A203832 A203833 A203834 * A203836 A203837 A203838

Keyword

nonn,tabl

Author

R. H. Hardin Jan 06 2012

Status

approved