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 A232316 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every element equal to some horizontal or antidiagonal neighbor, with top left element zero 14
 2, 5, 5, 16, 24, 13, 52, 139, 115, 34, 169, 853, 1202, 551, 89, 549, 5241, 14042, 10409, 2640, 233, 1784, 32089, 164014, 231454, 90157, 12649, 610, 5797, 196698, 1905436, 5142441, 3815483, 780922, 60605, 1597, 18837, 1205422, 22161823, 113293694 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts .....2.......5.........16............52..............169.................549 .....5......24........139...........853.............5241...............32089 ....13.....115.......1202.........14042...........164014.............1905436 ....34.....551......10409........231454..........5142441...........113293694 ....89....2640......90157.......3815483........161243887..........6736602042 ...233...12649.....780922......62897985.......5055954492........400571676322 ...610...60605....6764246....1036869496.....158534446141......23818815015639 ..1597..290376...58591124...17092731689....4971005036586....1416315842358249 ..4181.1391275..507509767..281772661177..155870804492221...84217060496525106 .10946.6665999.4395993154.4645005493684.4887484036570530.5007720081104988709 LINKS R. H. Hardin, Table of n, a(n) for n = 1..390 FORMULA Empirical for column k: k=1: a(n) = 3*a(n-1) -a(n-2) k=2: a(n) = 5*a(n-1) -a(n-2) k=3: a(n) = 10*a(n-1) -11*a(n-2) -5*a(n-3) -a(n-4) k=4: a(n) = 19*a(n-1) -44*a(n-2) +43*a(n-3) -19*a(n-4) +4*a(n-5) -2*a(n-6) for n>7 k=5: [order 12] for n>13 k=6: [order 18] for n>20 k=7: [order 37] for n>40 Empirical for row n: n=1: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>5 n=2: [order 12] for n>14 n=3: [order 32] for n>34 n=4: [order 78] for n>82 EXAMPLE Some.solutions.for.n=3.k=4 ..0..0..0..1..1....0..0..1..1..0....0..0..0..1..1....0..0..1..1..0 ..0..0..1..1..1....0..1..1..0..0....0..0..0..1..1....0..1..1..0..1 ..1..1..0..0..0....1..0..0..1..1....0..0..1..1..1....0..0..0..1..0 ..1..1..1..1..1....1..1..1..0..0....0..0..0..0..0....1..1..1..0..0 CROSSREFS Column 1 is A001519(n+1) Column 2 is A004254(n+1) Sequence in context: A063786 A121304 A002106 * A184604 A064630 A089793 Adjacent sequences: A232313 A232314 A232315 * A232317 A232318 A232319 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Nov 22 2013 STATUS approved

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Last modified March 26 21:04 EDT 2023. Contains 361552 sequences. (Running on oeis4.)