A295379 - OEIS

%I #4 Nov 21 2017 07:11:49

%S 2,3,3,5,8,5,8,19,19,8,13,48,74,48,13,21,120,278,278,120,21,34,299,

%T 1067,1634,1067,299,34,55,747,4071,9507,9507,4071,747,55,89,1865,

%U 15557,55643,85310,55643,15557,1865,89,144,4656,59407,325134,761795,761795,325134

%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 4 1s.

%C Table starts

%C ..2....3......5........8........13..........21............34.............55

%C ..3....8.....19.......48.......120.........299...........747...........1865

%C ..5...19.....74......278......1067........4071.........15557..........59407

%C ..8...48....278.....1634......9507.......55643........325134........1900380

%C .13..120...1067.....9507.....85310......761795.......6819658.......60996884

%C .21..299...4071....55643....761795....10437240.....142860055.....1956512289

%C .34..747..15557...325134...6819658...142860055....2995361770....62765357574

%C .55.1865..59407..1900380..60996884..1956512289...62765357574..2013609204094

%C .89.4656.226944.11107738.545729054.26790134422.1315649551906.64595519660126

%H R. H. Hardin, <a href="/A295379/b295379.txt">Table of n, a(n) for n = 1..311</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -a(n-4)

%F k=3: [order 10]

%F k=4: [order 25]

%F k=5: [order 70]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n+2).

%Y Column 2 is A295045.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 21 2017