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 A303624 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12

%I #4 Apr 27 2018 09:55:45

%S 1,1,2,1,2,4,1,12,2,8,1,20,38,3,16,1,72,68,148,6,32,1,168,362,325,616,

%T 10,64,1,496,1283,3591,1870,2520,21,128,1,1296,5411,19467,37910,10741,

%U 10288,42,256,1,3616,22516,160807,350410,398859,62207,42100,86,512,1,9760

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ...1..1......1.......1.........1...........1.............1................1

%C ...2..2.....12......20........72.........168...........496.............1296

%C ...4..2.....38......68.......362........1283..........5411............22516

%C ...8..3....148.....325......3591.......19467........160807..........1173612

%C ..16..6....616....1870.....37910......350410.......5249045.........70522741

%C ..32.10...2520...10741....398859.....6446485.....179884814.......4470005178

%C ..64.21..10288...62207...4288358...122517773....6323564388.....290118140045

%C .128.42..42100..363485..46208517..2348299355..224091914399...18955122420980

%C .256.86.172268.2135551.499581127.45211204167.7966090548780.1240883902751147

%H R. H. Hardin, <a href="/A303624/b303624.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 5*a(n-1) -5*a(n-2) +8*a(n-3) -12*a(n-4) +4*a(n-5) -4*a(n-6) for n>8

%F k=4: [order 22] for n>24

%F k=5: [order 62] for n>65

%F Empirical for row n:

%F n=1: a(n) = a(n-1)

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

%F n=3: [order 16] for n>17

%F n=4: [order 43] for n>44

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A240513(n-2).

%Y Row 2 is A302368.

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Apr 27 2018

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Last modified July 18 21:02 EDT 2024. Contains 374388 sequences. (Running on oeis4.)