cp's OEIS Frontend

A269011 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

%I A269011 #4 Feb 17 2016 12:04:50
%S A269011 0,1,0,2,4,0,5,8,15,0,10,36,46,48,0,20,88,305,224,145,0,38,272,1078,
%T A269011 2136,1066,420,0,71,696,4948,10976,14240,4952,1183,0,130,1900,18210,
%U A269011 73568,109058,91048,22654,3264,0,235,4856,73277,390064,1049588,1053432,566656
%N A269011 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
%C A269011 Table starts
%C A269011 .0.....1.......2.........5.........10...........20.............38
%C A269011 .0.....4.......8........36.........88..........272............696
%C A269011 .0....15......46.......305.......1078.........4948..........18210
%C A269011 .0....48.....224......2136......10976........73568.........390064
%C A269011 .0...145....1066.....14240.....109058......1049588........8134304
%C A269011 .0...420....4952.....91048....1053432.....14382480......164351184
%C A269011 .0..1183...22654....566656...10002542....192100836.....3258530608
%C A269011 .0..3264..102416...3456320...93733440...2516546784....63679868768
%C A269011 .0..8865..458674..20760192..869397882..32481770852..1230707111424
%C A269011 .0.23780.2038328.123186784.7996744280.414339126768.23573013881888
%H A269011 R. H. Hardin, <a href="/A269011/b269011.txt">Table of n, a(n) for n = 1..721</a>
%F A269011 Empirical for column k:
%F A269011 k=1: a(n) = a(n-1)
%F A269011 k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) -a(n-4)
%F A269011 k=3: a(n) = 10*a(n-1) -31*a(n-2) +24*a(n-3) +21*a(n-4) -18*a(n-5) -9*a(n-6)
%F A269011 k=4: a(n) = 12*a(n-1) -40*a(n-2) +8*a(n-3) +92*a(n-4) -32*a(n-5) -64*a(n-6) for n>7
%F A269011 k=5: [order 12]
%F A269011 k=6: [order 14]
%F A269011 k=7: [order 24] for n>25
%F A269011 Empirical for row n:
%F A269011 n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
%F A269011 n=2: a(n) = 2*a(n-1) +5*a(n-2) -6*a(n-3) -9*a(n-4)
%F A269011 n=3: a(n) = 4*a(n-1) +8*a(n-2) -34*a(n-3) -16*a(n-4) +60*a(n-5) -25*a(n-6)
%F A269011 n=4: [order 8]
%F A269011 n=5: [order 14]
%F A269011 n=6: [order 20]
%F A269011 n=7: [order 32]
%e A269011 Some solutions for n=4 k=4
%e A269011 ..1..1..0..0. .0..0..1..0. .1..0..1..1. .0..1..0..0. .0..0..0..0
%e A269011 ..0..0..0..1. .0..0..1..0. .1..0..0..0. .0..0..1..0. .1..0..0..0
%e A269011 ..0..0..0..0. .1..0..0..0. .1..0..0..1. .0..0..1..0. .0..1..0..0
%e A269011 ..0..1..0..1. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..1..0..0
%Y A269011 Column 2 is A093967.
%Y A269011 Row 1 is A001629.
%K A269011 nonn,tabl
%O A269011 1,4
%A A269011 _R. H. Hardin_, Feb 17 2016