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 A243729 T(n,k)=Number of length n+2 0..k arrays with no three unequal elements in a row and no three equal elements in a row and new values 0..k introduced in 0..k order 9
 3, 3, 5, 3, 6, 8, 3, 6, 12, 13, 3, 6, 12, 24, 21, 3, 6, 12, 25, 48, 34, 3, 6, 12, 25, 53, 96, 55, 3, 6, 12, 25, 53, 115, 192, 89, 3, 6, 12, 25, 53, 116, 253, 384, 144, 3, 6, 12, 25, 53, 116, 259, 564, 768, 233, 3, 6, 12, 25, 53, 116, 259, 593, 1268, 1536, 377, 3, 6, 12, 25, 53, 116, 259 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ...3....3....3....3....3....3....3....3....3....3....3....3....3....3....3....3 ...5....6....6....6....6....6....6....6....6....6....6....6....6....6....6....6 ...8...12...12...12...12...12...12...12...12...12...12...12...12...12...12...12 ..13...24...25...25...25...25...25...25...25...25...25...25...25...25...25...25 ..21...48...53...53...53...53...53...53...53...53...53...53...53...53...53...53 ..34...96..115..116..116..116..116..116..116..116..116..116..116..116..116..116 ..55..192..253..259..259..259..259..259..259..259..259..259..259..259..259..259 ..89..384..564..593..594..594..594..594..594..594..594..594..594..594..594..594 .144..768.1268.1382.1389.1389.1389.1389.1389.1389.1389.1389.1389.1389.1389.1389 .233.1536.2871.3281.3322.3323.3323.3323.3323.3323.3323.3323.3323.3323.3323.3323 LINKS R. H. Hardin, Table of n, a(n) for n = 1..9999 FORMULA Empirical for column k: k=1: a(n) = a(n-1) +a(n-2) k=2: a(n) = 2*a(n-1) k=3: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -3*a(n-4) k=4: a(n) = 4*a(n-1) -13*a(n-3) +6*a(n-4) +8*a(n-5) k=5: a(n) = 5*a(n-1) -29*a(n-3) +20*a(n-4) +51*a(n-5) -31*a(n-6) -30*a(n-7) k=6: [order 9] k=7: [order 11] k=8: [order 13] k=9: [order 15] EXAMPLE Some solutions for n=6 k=4 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0 ..0....0....0....0....1....1....1....1....1....1....1....1....1....0....1....0 ..1....1....1....1....1....1....0....0....1....1....1....1....0....1....0....1 ..1....1....0....0....0....2....1....1....2....2....2....2....0....0....1....1 ..0....2....1....1....0....2....0....1....2....2....2....1....2....1....0....0 ..0....2....1....0....2....3....1....2....0....3....1....2....2....0....0....1 ..1....3....2....1....2....3....1....1....0....2....1....2....3....0....2....1 ..0....2....1....1....0....0....0....2....1....3....2....0....3....2....0....2 CROSSREFS Column 1 is A000045(n+3) Column 2 is A003945 Sequence in context: A057662 A015971 A163167 * A200810 A365710 A114003 Adjacent sequences: A243726 A243727 A243728 * A243730 A243731 A243732 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Jun 09 2014 STATUS approved

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Last modified February 25 11:24 EST 2024. Contains 370325 sequences. (Running on oeis4.)