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A300973 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7

%I

%S 0,1,1,1,3,1,2,11,11,2,3,37,72,37,3,5,129,459,459,129,5,8,450,2956,

%T 5362,2956,450,8,13,1568,18996,63565,63565,18996,1568,13,21,5464,

%U 122043,753471,1396701,753471,122043,5464,21,34,19041,784108,8926774,30679527

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 6 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......72........459.........2956..........18996............122043

%C ..2....37.....459.......5362........63565.........753471...........8926774

%C ..3...129....2956......63565......1396701.......30679527.........673550354

%C ..5...450...18996.....753471.....30679527.....1248976325.......50812633429

%C ..8..1568..122043....8926774....673550354....50812633429.....3830408271334

%C .13..5464..784108..105763972..14787165263..2067233940661...288757143760689

%C .21.19041.5037730.1253091915.324641851765.84103618035068.21768367076769721

%H R. H. Hardin, <a href="/A300973/b300973.txt">Table of n, a(n) for n = 1..241</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 9] for n>11

%F k=4: [order 41] for n>42

%e Some solutions for n=5 k=4

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

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

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

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

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

%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 17 2018

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Last modified October 21 01:38 EDT 2021. Contains 348132 sequences. (Running on oeis4.)