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A296396 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 or 3 neighboring 1s. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)