A203934 T(n,k)=Number of (n+1)X(k+1) 0..5 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements

396, 4356, 4356, 47916, 106596, 47916, 527076, 2543436, 2543436, 527076, 5797836, 60873876, 140120856, 60873876, 5797836, 63776196, 1456391916, 7748585676, 7748585676, 1456391916, 63776196, 701538156, 34845401556, 428652828396

Offset

1,1

Comments

Table starts

........396...........4356.............47916................527076

.......4356.........106596...........2543436..............60873876

......47916........2543436.........140120856............7748585676

.....527076.......60873876........7748585676.........1012872412476

....5797836.....1456391916......428652828396.......132923754354276

...63776196....34845401556....23714024087016.....17475349695161076

..701538156...833700866796..1311917257647036...2297197186864332876

.7716919716.19946896311636.72578467770478956.302046352349437619676

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for row k:

k=1: a(n) = 36*11^n

k=2: a(n) = 21*a(n-1) +70*a(n-2)

k=3: a(n) = 61*a(n-1) -315*a(n-2) +50*a(n-3)

k=4: a(n) = 91*a(n-1) +7335*a(n-2) -264625*a(n-3) -85500*a(n-4) +10470000*a(n-5) +2475000*a(n-6) -20750000*a(n-7)

k=5: (order 12 recurrence)

Example

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

Crossrefs

Sequence in context: A275171 A028299 A205628 * A203927 A205330 A092720

Adjacent sequences: A203931 A203932 A203933 * A203935 A203936 A203937

Keyword

nonn,tabl

Author

R. H. Hardin Jan 08 2012

Status

approved