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 A318098 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7

%I #4 Aug 16 2018 10:31:44

%S 0,1,1,1,5,1,2,16,16,2,3,50,45,50,3,5,160,220,220,160,5,8,511,795,

%T 1563,795,511,8,13,1634,3310,9193,9193,3310,1634,13,21,5226,12774,

%U 57744,73788,57744,12774,5226,21,34,16716,51298,356786,679923,679923,356786,51298

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

%C Table starts

%C ..0.....1......1........2.........3...........5............8.............13

%C ..1.....5.....16.......50.......160.........511.........1634...........5226

%C ..1....16.....45......220.......795........3310........12774..........51298

%C ..2....50....220.....1563......9193.......57744.......356786........2215533

%C ..3...160....795.....9193.....73788......679923......5965933.......53097417

%C ..5...511...3310....57744....679923.....8985801....114914085.....1478603982

%C ..8..1634..12774...356786...5965933...114914085...2154127036....40412593332

%C .13..5226..51298..2215533..53097417..1478603982..40412593332..1097965368750

%C .21.16716.201637.13752047.470312224.19018066407.760353849044.29957208854824

%H R. H. Hardin, <a href="/A318098/b318098.txt">Table of n, a(n) for n = 1..198</a>

%F Empirical for column k:

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

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

%F k=3: [order 19] for n>21

%F k=4: [order 72] for n>73

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A317817.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Aug 16 2018

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Last modified December 10 00:12 EST 2023. Contains 367696 sequences. (Running on oeis4.)