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 A269276 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once. 14
 0, 4, 0, 24, 108, 0, 108, 1368, 1620, 0, 432, 13896, 46872, 20412, 0, 1620, 127512, 1104264, 1365336, 236196, 0, 5832, 1104264, 23549400, 74853576, 36673560, 2598156, 0, 20412, 9211608, 474819408, 3719884392, 4684312584, 938176344 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts .0........4..........24............108...............432................1620 .0......108........1368..........13896............127512.............1104264 .0.....1620.......46872........1104264..........23549400...........474819408 .0....20412.....1365336.......74853576........3719884392........174924572760 .0...236196....36673560.....4684312584......542973139128......59587625651904 .0..2598156...938176344...279339197256....75556007986536...19356924219624936 .0.27634932.23230366488.16128206816904.10181956012212600.6090616046325570480 LINKS R. H. Hardin, Table of n, a(n) for n = 1..241 FORMULA Empirical for column k: k=1: a(n) = 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..0..1. .0..0..0..0. .0..2..0..0. .0..0..0..0. .0..0..2..0 ..0..2..3..1. .2..2..0..0. .2..2..3..1. .2..0..2..1. .0..2..2..3 ..2..1..0..2. .3..2..1..1. .0..1..0..2. .0..0..1..3. .3..1..1..0 CROSSREFS Row 1 is A120908. Sequence in context: A357810 A057402 A269214 * A359521 A172394 A172395 Adjacent sequences: A269273 A269274 A269275 * A269277 A269278 A269279 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Feb 21 2016 STATUS approved

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Last modified January 27 13:44 EST 2023. Contains 359844 sequences. (Running on oeis4.)