A269767 T(n,k)=Number of nXk 0..5 arrays with some element plus some horizontally or vertically adjacent neighbor totalling five exactly once.

0, 6, 6, 60, 480, 60, 450, 17520, 17520, 450, 3000, 524160, 2624640, 524160, 3000, 18750, 14288400, 326697720, 326697720, 14288400, 18750, 112500, 368958240, 37212131520, 170119348800, 37212131520, 368958240, 112500, 656250, 9195061680

Offset

1,2

Comments

Table starts

.....0.........6............60...............450..................3000

.....6.......480.........17520............524160..............14288400

....60.....17520.......2624640.........326697720...........37212131520

...450....524160.....326697720......170119348800........81208264293720

..3000..14288400...37212131520....81208264293720....162622227315688800

.18750.368958240.4022791852800.36821411380183680.309460647800786666280

Links

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

Formula

Empirical for column k:

k=1: a(n) = 10*a(n-1) -25*a(n-2)

k=2: a(n) = 42*a(n-1) -441*a(n-2) for n>3

k=3: a(n) = 184*a(n-1) -9134*a(n-2) +61640*a(n-3) -112225*a(n-4) for n>5

k=4: [order 6] for n>7

k=5: [order 14] for n>15

k=6: [order 26] for n>27

k=7: [order 64] for n>65

Example

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

Crossrefs

Sequence in context: A074949 A078290 A269888 * A065239 A146892 A347916

Adjacent sequences: A269764 A269765 A269766 * A269768 A269769 A269770

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 04 2016

Status

approved