A268798 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

0, 3, 3, 12, 22, 12, 36, 78, 78, 36, 96, 234, 248, 234, 96, 240, 652, 950, 950, 652, 240, 576, 1714, 3384, 4800, 3384, 1714, 576, 1344, 4360, 11948, 23994, 23994, 11948, 4360, 1344, 3072, 10820, 41248, 117062, 168740, 117062, 41248, 10820, 3072, 6912, 26366

Offset: 1

Author

R. H. Hardin, Feb 13 2016

Keywords

• nonn
• tabl

Comments

Table starts

....0.....3......12.......36.........96.........240...........576

....3....22......78......234........652........1714..........4360

...12....78.....248......950.......3384.......11948.........41248

...36...234.....950.....4800......23994......117062........561116

...96...652....3384....23994.....168740.....1158904.......7801688

..240..1714...11948...117062....1158904....11138352.....104971262

..576..4360...41248...561116....7801688...104971262....1384570516

.1344.10820..140698..2652936...51781418...974000420...17967375416

.3072.26366..474472.12405748..339641264..8927994302..230262982692

.6912.63346.1586038.57490444.2206871084.81031120788.2921020155826

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..637

Crossrefs

Column 1 is A167667(n-1).

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -4*a(n-2)

k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) -a(n-6) for n>7

k=3: [order 10] for n>12

k=4: [order 16] for n>19

k=5: [order 26] for n>29

k=6: [order 42] for n>45

k=7: [order 68] for n>71