A203887 T(n,k)=Number of (n+1)X(k+1) 0..6 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements

637, 8281, 8281, 107653, 254359, 107653, 1399489, 7501753, 7501753, 1399489, 18193357, 222645367, 543848893, 222645367, 18193357, 236513641, 6601376089, 39572771665, 39572771665, 6601376089, 236513641, 3074677333, 195759462871

Offset

1,1

Comments

Table starts

.........637............8281..............107653..............1399489

........8281..........254359.............7501753............222645367

......107653.........7501753...........543848893..........39572771665

.....1399489.......222645367.........39572771665........7265109130279

....18193357......6601376089.......2880436707253.....1337957259758497

...236513641....195759462871.....209668438383145...247090069595954263

..3074677333...5804976472057...15261911634884845.45601045546133880817

.39970805329.172139217677623.1110925438997643073

Links

R. H. Hardin, Table of n, a(n) for n = 1..60

Formula

Empirical for columns:

k=1: a(n) = 49*13^n

k=2: a(n) = 25*a(n-1) +138*a(n-2)

k=3: a(n) = 79*a(n-1) -450*a(n-2) -144*a(n-3)

k=4: a(n) = 115*a(n-1) +17016*a(n-2) -763308*a(n-3) -1177416*a(n-4) +49714560*a(n-5) +35870688*a(n-6) -153031680*a(n-7)

k=5: (order 12 recurrence)

Example

Some solutions for n=4 k=3
..4..6..2..0....2..5..1..0....1..1..5..2....6..6..4..0....6..0..3..3
..5..4..6..2....1..2..5..1....3..1..1..5....4..6..6..4....3..6..0..3
..6..5..4..6....0..1..2..5....2..3..1..1....5..4..6..6....1..3..6..0
..2..6..5..4....6..0..1..2....4..2..3..1....3..5..4..6....6..1..3..6
..4..2..6..5....2..6..0..1....0..4..2..3....1..3..5..4....3..6..1..3

Crossrefs

Sequence in context: A198774 A043483 A203042 * A203880 A250465 A203879

Adjacent sequences: A203884 A203885 A203886 * A203888 A203889 A203890

Keyword

nonn,tabl

Author

R. H. Hardin Jan 07 2012

Status

approved