A296396 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 or 3 neighboring 1s.

1, 2, 2, 3, 6, 3, 4, 11, 11, 4, 6, 28, 36, 28, 6, 9, 63, 115, 115, 63, 9, 13, 139, 387, 597, 387, 139, 13, 19, 328, 1280, 2969, 2969, 1280, 328, 19, 28, 735, 4237, 14502, 21769, 14502, 4237, 735, 28, 41, 1684, 14026, 72069, 159732, 159732, 72069, 14026, 1684, 41, 60

Offset

1,2

Comments

Table starts

..1....2.....3.......4........6..........9..........13............19

..2....6....11......28.......63........139.........328...........735

..3...11....36.....115......387.......1280........4237.........14026

..4...28...115.....597.....2969......14502.......72069........355733

..6...63...387....2969....21769.....159732.....1181174.......8690359

..9..139..1280...14502...159732....1740403....19142885.....209776696

.13..328..4237...72069..1181174...19142885...313843472....5120370505

.19..735.14026..355733..8690359..209776696..5120370505..124433749976

.28.1684.46454.1758440.64100854.2301194495.83668287300.3028311394674

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-3)

k=2: a(n) = a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) +4*a(n-5) -a(n-6) -4*a(n-7) +a(n-9)

k=3: [order 14]

k=4: [order 49]

Example

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

Crossrefs

Column 1 is A000930(n+1).

Sequence in context: A290632 A291543 A296320 * A125102 A003506 A047662

Adjacent sequences: A296393 A296394 A296395 * A296397 A296398 A296399

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 11 2017

Status

approved