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 A269289 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once. 13
 4, 16, 16, 60, 216, 64, 216, 2124, 2592, 256, 756, 19188, 62748, 29160, 1024, 2592, 164556, 1363572, 1698732, 314928, 4096, 8748, 1363572, 27788292, 87559668, 43674876, 3306744, 16384, 29160, 11026764, 544118148, 4204943820, 5306911092 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ......4.........16.............60...............216...................756 .....16........216...........2124.............19188................164556 .....64.......2592..........62748...........1363572..............27788292 ....256......29160........1698732..........87559668............4204943820 ...1024.....314928.......43674876........5306911092..........598478857956 ...4096....3306744.....1085203980......309846524148........81907569617580 ..16384...34012224....26317946844....17623065834612.....10908770041709316 ..65536..344373768...626778812268...983118947312628...1424067311317705740 .262144.3443737680.14718495557052.54032675767734132.183070424003703987492 LINKS R. H. Hardin, Table of n, a(n) for n = 1..241 FORMULA Empirical for column k: k=1: a(n) = 4*a(n-1) k=2: a(n) = 18*a(n-1) -81*a(n-2) k=3: a(n) = 42*a(n-1) -441*a(n-2) k=4: a(n) = 98*a(n-1) -2401*a(n-2) for n>3 k=5: a(n) = 234*a(n-1) -14277*a(n-2) +68796*a(n-3) -86436*a(n-4) k=6: [order 6] for n>7 k=7: [order 10] for n>11 Empirical for row n: n=1: a(n) = 6*a(n-1) -9*a(n-2) n=2: a(n) = 14*a(n-1) -49*a(n-2) for n>4 n=3: a(n) = 36*a(n-1) -378*a(n-2) +972*a(n-3) -729*a(n-4) for n>7 n=4: [order 8] for n>12 n=5: [order 18] for n>23 n=6: [order 40] for n>46 EXAMPLE Some solutions for n=3 k=4 ..0..2..3..3. .0..2..3..1. .0..0..0..1. .0..2..2..2. .2..0..0..2 ..2..1..3..1. .2..1..0..2. .2..2..3..1. .0..2..0..0. .0..0..3..3 ..3..1..0..1. .1..0..2..0. .1..3..3..3. .2..0..0..2. .0..1..1..0 CROSSREFS Column 1 is A000302. Column 2 is A159739(n+1). Row 1 is A120926(n+1). Sequence in context: A269143 A269109 A269201 * A267933 A206974 A206577 Adjacent sequences: A269286 A269287 A269288 * A269290 A269291 A269292 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Feb 21 2016 STATUS approved

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Last modified May 29 19:17 EDT 2023. Contains 363042 sequences. (Running on oeis4.)