A269888 T(n,k)=Number of nXk 0..5 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling five exactly once.

0, 6, 6, 60, 432, 60, 450, 11280, 11280, 450, 3000, 250992, 943488, 250992, 3000, 18750, 5125008, 68182800, 68182800, 5125008, 18750, 112500, 99482544, 4546948272, 16086672048, 4546948272, 99482544, 112500, 656250, 1867222224

Offset

1,2

Comments

Table starts

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

......6........432..........11280.............250992................5125008

.....60......11280.........943488...........68182800.............4546948272

....450.....250992.......68182800........16086672048..........3515869538472

...3000....5125008.....4546948272......3515869538472.......2524680110862912

..18750...99482544...288987039048....733651366146384....1733054018904626400

.112500.1867222224.17784013336560.148379658813705408.1153865935196746139616

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

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

k=2: a(n) = 30*a(n-1) -197*a(n-2) -420*a(n-3) -196*a(n-4) for n>5

k=3: [order 10] for n>11

k=4: [order 28] for n>29

Example

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

Crossrefs

Column 1 is A269760.

Sequence in context: A321971 A074949 A078290 * A269767 A065239 A146892

Adjacent sequences: A269885 A269886 A269887 * A269889 A269890 A269891

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 06 2016

Status

approved