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 A280673 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards. 11
 1, 2, 2, 4, 11, 5, 11, 59, 82, 14, 30, 338, 858, 612, 41, 82, 1917, 10205, 12484, 4568, 122, 224, 10893, 119440, 310365, 181640, 34096, 365, 612, 61880, 1401470, 7533245, 9439606, 2642832, 254496, 1094, 1672, 351541, 16438612, 183331502, 474736149 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ....1.........2............4..............11...............30................82 ....2........11...........59.............338.............1917.............10893 ....5........82..........858...........10205...........119440...........1401470 ...14.......612........12484..........310365..........7533245.........183331502 ...41......4568.......181640.........9439606........474736149.......23952262535 ..122.....34096......2642832.......287101721......29920114246.....3130289979912 ..365....254496.....38452768......8732086113....1885698283255...409089889172506 .1094...1899584....559481408....265582964074..118845116023725.53463025958093933 .3281..14178688...8140361856...8077601392565.7490149091439288 .9842.105831168.118440917248.245677069239189 LINKS R. H. Hardin, Table of n, a(n) for n = 1..97 FORMULA Empirical for column k: k=1: a(n) = 4*a(n-1) -3*a(n-2) k=2: a(n) = 8*a(n-1) -4*a(n-2) for n>3 k=3: a(n) = 14*a(n-1) +8*a(n-2) k=4: a(n) = 29*a(n-1) +44*a(n-2) -27*a(n-3) -81*a(n-4) for n>5 k=5: [order 8] for n>9 k=6: [order 20] for n>22 Empirical for row n: n=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4 n=2: a(n) = 5*a(n-1) +6*a(n-2) -11*a(n-3) -7*a(n-4) +4*a(n-5) for n>6 n=3: [order 18] for n>20 n=4: [order 73] for n>78 EXAMPLE Some solutions for n=3 k=4 ..0..1..0..0. .0..1..0..2. .0..1..0..1. .0..0..1..0. .0..1..1..0 ..0..1..2..1. .2..0..2..1. .0..2..1..0. .2..2..1..1. .2..0..2..0 ..1..2..0..0. .2..1..0..2. .2..0..2..0. .1..0..2..2. .1..0..1..1 CROSSREFS Column 1 is A007051(n-1). Column 2 is A209094. Row 1 is A021006(n-3). Sequence in context: A219985 A220800 A220786 * A067920 A280531 A072074 Adjacent sequences:  A280670 A280671 A280672 * A280674 A280675 A280676 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Jan 07 2017 STATUS approved

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Last modified September 23 04:54 EDT 2020. Contains 337295 sequences. (Running on oeis4.)