A295253 - OEIS

A295253

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

2, 4, 4, 7, 11, 7, 13, 35, 35, 13, 24, 106, 183, 106, 24, 44, 327, 948, 948, 327, 44, 81, 1003, 4928, 8271, 4928, 1003, 81, 149, 3082, 25596, 72745, 72745, 25596, 3082, 149, 274, 9465, 132993, 638779, 1081924, 638779, 132993, 9465, 274, 504, 29073, 690938

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Table starts

...2.....4.......7........13..........24............44..............81

...4....11......35.......106.........327..........1003............3082

...7....35.....183.......948........4928.........25596..........132993

..13...106.....948......8271.......72745........638779.........5611444

..24...327....4928.....72745.....1081924......16064421.......238620900

..44..1003...25596....638779....16064421.....403318354.....10130231034

..81..3082..132993...5611444...238620900...10130231034....430246838462

.149..9465..690938..49287776..3544087017..254413406815..18271078872449

.274.29073.3589717.432936397.52640098668.6389646907183.775938327252984

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..263

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) +a(n-3)

k=2: a(n) = 2*a(n-1) +3*a(n-2) +a(n-3) -a(n-5)

k=3: [order 18]

k=4: [order 45]

EXAMPLE

Some solutions for n=4 k=4

..0..0..1..0. .0..1..1..1. .0..0..0..1. .1..1..0..1. .1..0..0..1

..0..1..0..0. .0..0..1..0. .0..1..0..1. .0..0..0..0. .0..0..0..0

..0..0..0..1. .0..1..0..0. .1..0..0..0. .1..1..0..0. .1..0..1..0

..0..0..0..1. .0..1..0..0. .0..1..0..0. .0..0..0..0. .1..0..1..0

CROSSREFS

Column 1 is A000073(n+3).

Sequence in context: A268750 A282996 A295275 * A295652 A269075 A283543

Adjacent sequences: A295250 A295251 A295252 * A295254 A295255 A295256

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 18 2017

STATUS

approved