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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 A169717 A246420

Adjacent sequences:  A203832 A203833 A203834 * A203836 A203837 A203838

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Jan 06 2012

STATUS

approved

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Last modified October 24 06:31 EDT 2014. Contains 248502 sequences.