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 A302367 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 13

%I #4 Apr 06 2018 12:21:15

%S 1,1,2,1,2,4,1,12,2,8,1,20,31,3,16,1,72,20,109,6,32,1,168,154,77,397,

%T 10,64,1,496,284,918,209,1430,21,128,1,1296,1109,3125,6580,774,5110,

%U 42,256,1,3616,3472,21831,26458,49293,3143,18395,86,512,1,9760,12763,125193

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 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....31....20......154.......284........1109..........3472

%C ...8..3...109....77......918......3125.......21831........125193

%C ..16..6...397...209.....6580.....26458......405340.......3462040

%C ..32.10..1430...774....49293....330505.....9361759.....134269527

%C ..64.21..5110..3143...367512...3858625...188443738....4558781926

%C .128.42.18395.13556..2856621..48375470..4174802035..169314399506

%C .256.86.66203.60280.22185382.608124211.91302504318.6186362081201

%H R. H. Hardin, <a href="/A302367/b302367.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: [order 12]

%F k=4: [order 50] for n>53

%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>18

%F n=4: [order 63] for n>66

%e Some solutions for n=5 k=4

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

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

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

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

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

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

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

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Apr 06 2018

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Last modified August 13 12:15 EDT 2024. Contains 375139 sequences. (Running on oeis4.)