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A300930 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7

%I

%S 0,1,1,1,3,1,2,11,11,2,3,37,75,37,3,5,129,508,508,129,5,8,450,3447,

%T 6638,3447,450,8,13,1568,23404,87561,87561,23404,1568,13,21,5464,

%U 158855,1155263,2244335,1155263,158855,5464,21,34,19041,1078231,15238332

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ..0.....1.......1..........2............3...............5..................8

%C ..1.....3......11.........37..........129.............450...............1568

%C ..1....11......75........508.........3447...........23404.............158855

%C ..2....37.....508.......6638........87561.........1155263...........15238332

%C ..3...129....3447......87561......2244335........57594572.........1477281166

%C ..5...450...23404....1155263.....57594572......2875574552.......143498589629

%C ..8..1568..158855...15238332...1477281166....143498589629.....13930396115571

%C .13..5464.1078231..200997959..37892542998...7160975085336...1352339873296663

%C .21.19041.7318522.2651226860.971951600750.357354070296570.131283287305824217

%H R. H. Hardin, <a href="/A300930/b300930.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) = 4*a(n-1) -2*a(n-2) +a(n-3) -a(n-4) for n>5

%F k=3: [order 8] for n>10

%F k=4: [order 26] for n>27

%F k=5: [order 64] for n>67

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n-1).

%Y Column 2 is A232031(n-1).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Mar 15 2018

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Last modified November 28 12:45 EST 2021. Contains 349403 sequences. (Running on oeis4.)