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 A255622 T(n,k)=Number of length n+k 0..2 arrays with at most two downsteps in every k consecutive neighbor pairs 12
 9, 27, 27, 81, 81, 81, 237, 243, 243, 243, 651, 694, 729, 729, 729, 1647, 1803, 2040, 2187, 2187, 2187, 3834, 4248, 5088, 5997, 6561, 6561, 6561, 8272, 9186, 11386, 14381, 17622, 19683, 19683, 19683, 16698, 18483, 23298, 30816, 40659, 51768, 59049, 59049 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ......9.....27......81.....237.....651.....1647.....3834.....8272....16698 .....27.....81.....243.....694....1803.....4248.....9186....18483....35016 .....81....243.....729....2040....5088....11386....23298....44361....79692 ....243....729....2187....5997...14381....30816....60390...110270...190269 ....729...2187....6561...17622...40659....83325...156563...275166...458604 ...2187...6561...19683...51768..114546...225253...405687...685713..1103630 ...6561..19683...59049..152106..322078...602886..1047141..1706242..2653107 ..19683..59049..177147..446932..907110..1605726..2656032..4203558..6343974 ..59049.177147..531441.1313199.2556858..4293918..6682971.10111362.14922893 .177147.531441.1594323.3858468.7205734.11529741.16925280.24065191.34121019 LINKS R. H. Hardin, Table of n, a(n) for n = 1..9999 FORMULA Empirical for column k: k=1: a(n) = 3*a(n-1) k=2: a(n) = 3*a(n-1) k=3: a(n) = 3*a(n-1) k=4: a(n) = 3*a(n-1) -a(n-3) +3*a(n-4) -3*a(n-5) -8*a(n-6) +9*a(n-7) -3*a(n-8) +a(n-9) k=5: [order 14] k=6: [order 20] k=7: [order 30] Empirical for row n: n=1: [polynomial of degree 8] n=2: [polynomial of degree 8] n=3: [polynomial of degree 8] n=4: [polynomial of degree 8] for n>2 n=5: [polynomial of degree 8] for n>3 n=6: [polynomial of degree 8] for n>4 n=7: [polynomial of degree 8] for n>5 EXAMPLE Some solutions for n=4 k=4 ..0....0....0....1....1....1....2....0....0....1....2....2....0....0....1....0 ..2....0....0....0....2....2....2....2....1....1....1....0....0....0....1....0 ..1....0....2....1....1....0....0....0....2....0....2....2....2....2....1....1 ..1....1....1....2....2....2....1....1....2....2....2....1....1....0....1....0 ..2....2....0....2....0....0....1....2....0....0....2....2....1....1....0....2 ..2....2....0....2....1....0....2....2....1....1....0....1....2....1....1....1 ..1....0....1....2....1....2....2....1....2....2....1....2....0....1....2....2 ..2....2....0....2....0....1....0....2....0....1....2....1....0....2....2....2 CROSSREFS Column 1 is A000244(n+1) Column 2 is A000244(n+2) Column 3 is A000244(n+3) Sequence in context: A010817 A205973 A122985 * A209511 A115148 A022701 Adjacent sequences:  A255619 A255620 A255621 * A255623 A255624 A255625 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Feb 28 2015 STATUS approved

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Last modified May 14 09:34 EDT 2021. Contains 343879 sequences. (Running on oeis4.)