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%I #4 Feb 17 2016 07:27:06
%S 2,4,4,7,13,8,13,35,41,16,23,103,174,126,32,41,278,805,849,379,64,72,
%T 763,3331,6009,4083,1121,128,126,2037,14080,37987,43512,19416,3272,
%U 256,219,5421,57287,244397,421450,308112,91491,9449,512,379,14264,232449,1506570
%N T(n,k)=Number of nXk binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
%C Table starts
%C ....2.....4.......7........13..........23............41..............72
%C ....4....13......35.......103.........278...........763............2037
%C ....8....41.....174.......805........3331.........14080...........57287
%C ...16...126.....849......6009.......37987........244397.........1506570
%C ...32...379....4083.....43512......421450.......4097199........38241770
%C ...64..1121...19416....308112.....4583103......66954420.......946498448
%C ..128..3272...91491...2144780....49084071....1073436321.....22995344760
%C ..256..9449..427863..14730784...519385102...16957258387....550731432312
%C ..512.27049.1988142.100087792..5442503771..264744926212..13040291111728
%C .1024.76866.9187653.674045392.56571775611.4093941136805.305911647779632
%H R. H. Hardin, <a href="/A268995/b268995.txt">Table of n, a(n) for n = 1..799</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)
%F k=3: a(n) = 10*a(n-1) -31*a(n-2) +30*a(n-3) -9*a(n-4)
%F k=4: a(n) = 16*a(n-1) -88*a(n-2) +200*a(n-3) -208*a(n-4) +96*a(n-5) -16*a(n-6) for n>7
%F k=5: [order 8] for n>9
%F k=6: [order 10] for n>12
%F k=7: [order 14] for n>16
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
%F n=2: a(n) = 2*a(n-1) +5*a(n-2) -4*a(n-3) -11*a(n-4) -6*a(n-5) -a(n-6)
%F n=3: [order 9]
%F n=4: [order 16]
%F n=5: [order 26]
%F n=6: [order 42]
%F n=7: [order 68]
%e Some solutions for n=4 k=4
%e ..1..1..0..1. .1..0..0..1. .0..0..0..0. .0..0..1..0. .0..0..0..1
%e ..0..0..0..1. .1..1..0..1. .0..1..0..0. .1..0..1..0. .0..0..0..1
%e ..0..1..0..1. .0..0..0..0. .0..1..0..1. .1..0..0..0. .0..0..1..0
%e ..0..0..0..0. .1..0..1..0. .0..0..0..0. .1..0..1..0. .1..0..1..0
%Y Column 1 is A000079.
%Y Row 1 is A208354(n+1).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 17 2016
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