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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 1 is A167667(n-1).

Sequence in context: A290438 A006804 A052533 * A136533 A268639 A192307

Adjacent sequences: A268795 A268796 A268797 * A268799 A268800 A268801

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 13 2016

Status

approved