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 A295253 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 3 1s. 8

%I

%S 2,4,4,7,11,7,13,35,35,13,24,106,183,106,24,44,327,948,948,327,44,81,

%T 1003,4928,8271,4928,1003,81,149,3082,25596,72745,72745,25596,3082,

%U 149,274,9465,132993,638779,1081924,638779,132993,9465,274,504,29073,690938

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

%C Table starts

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

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

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

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

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

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

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

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

%C .274.29073.3589717.432936397.52640098668.6389646907183.775938327252984

%H R. H. Hardin, <a href="/A295253/b295253.txt">Table of n, a(n) for n = 1..263</a>

%F Empirical for column k:

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

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

%F k=3: [order 18]

%F k=4: [order 45]

%e Some solutions for n=4 k=4

%e ..0..0..1..0. .0..1..1..1. .0..0..0..1. .1..1..0..1. .1..0..0..1

%e ..0..1..0..0. .0..0..1..0. .0..1..0..1. .0..0..0..0. .0..0..0..0

%e ..0..0..0..1. .0..1..0..0. .1..0..0..0. .1..1..0..0. .1..0..1..0

%e ..0..0..0..1. .0..1..0..0. .0..1..0..0. .0..0..0..0. .1..0..1..0

%Y Column 1 is A000073(n+3).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 18 2017

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Last modified December 4 15:36 EST 2021. Contains 349526 sequences. (Running on oeis4.)