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A295606 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2, 3 or 4 1s. 7

%I

%S 2,3,3,5,8,5,8,20,20,8,13,51,83,51,13,21,132,338,338,132,21,34,341,

%T 1425,2305,1425,341,34,55,883,6080,16340,16340,6080,883,55,89,2293,

%U 26249,119371,201602,119371,26249,2293,89,144,5964,114298,892086,2594128

%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2, 3 or 4 1s.

%C Table starts

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

%C ..3....8.....20.......51........132..........341.............883

%C ..5...20.....83......338.......1425.........6080...........26249

%C ..8...51....338.....2305......16340.......119371..........892086

%C .13..132...1425....16340.....201602......2594128........34416318

%C .21..341...6080...119371....2594128.....59562253......1412108105

%C .34..883..26249...892086...34416318...1412108105.....59768294027

%C .55.2293.114298..6775059..465449155..34084604345...2568256527624

%C .89.5964.501405.52046892.6367873016.830405539405.111128604535696

%H R. H. Hardin, <a href="/A295606/b295606.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical for column k:

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

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

%F k=3: [order 12]

%F k=4: [order 27]

%F k=5: [order 69]

%e Some solutions for n=4 k=4

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

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

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

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

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

%Y Column 2 is A295346.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 24 2017

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Last modified July 12 04:30 EDT 2020. Contains 335658 sequences. (Running on oeis4.)