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 A255107 T(n,k)=Number of length n+k 0..2 arrays with at most one downstep in every k consecutive neighbor pairs 13
 9, 26, 27, 66, 75, 81, 147, 168, 216, 243, 294, 331, 441, 622, 729, 540, 597, 789, 1137, 1791, 2187, 927, 1008, 1302, 1905, 2907, 5157, 6561, 1507, 1616, 2032, 2951, 4429, 7498, 14849, 19683, 2343, 2484, 3042, 4338, 6582, 10125, 19338, 42756, 59049, 3510 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ......9.....26.....66....147....294....540....927...1507...2343...3510...5096 .....27.....75....168....331....597...1008...1616...2484...3687...5313...7464 .....81....216....441....789...1302...2032...3042...4407...6215...8568..11583 ....243....622...1137...1905...2951...4338...6141...8448..11361..14997..19489 ....729...1791...2907...4429...6582...9297..12662..16779..21765..27753..34893 ...2187...5157...7498..10125..14001..19263..25578..33063..41851..52092..63954 ...6561..14849..19338..23463..29147..38010..49611..63075..78552..96210.116236 ..19683..42756..49698..55246..61542..73278..91887.115470.142200.172264.205869 ..59049.123111.127871.129480.133392.143045.166290.202716.247600.297597.352935 .177147.354484.329325.300432.292534.288057.303969.348070.415308.496188.585101 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) -a(n-3) k=3: a(n) = 3*a(n-1) -3*a(n-2) +8*a(n-3) -9*a(n-4) +3*a(n-5) -a(n-6) k=4: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +12*a(n-4) -18*a(n-5) +7*a(n-6) -3*a(n-8) +a(n-9) k=5: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +18*a(n-5) -29*a(n-6) +12*a(n-7) -6*a(n-10) +3*a(n-11) k=6: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +25*a(n-6) -42*a(n-7) +18*a(n-8) -10*a(n-12) +6*a(n-13) k=7: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +33*a(n-7) -57*a(n-8) +25*a(n-9) -15*a(n-14) +10*a(n-15) Empirical for row n: n=1: a(n) = (1/120)*n^5 + (1/6)*n^4 + (19/24)*n^3 + (11/6)*n^2 + (16/5)*n + 3 n=2: a(n) = (1/120)*n^5 + (5/24)*n^4 + (37/24)*n^3 + (175/24)*n^2 + (239/20)*n + 6 n=3: a(n) = (1/120)*n^5 + (1/4)*n^4 + (59/24)*n^3 + (93/4)*n^2 + (1321/30)*n + 11 n=4: a(n) = (1/120)*n^5 + (7/24)*n^4 + (85/24)*n^3 + (1505/24)*n^2 + (2809/20)*n + 30 for n>2 n=5: a(n) = (1/120)*n^5 + (1/3)*n^4 + (115/24)*n^3 + (889/6)*n^2 + (3867/10)*n + 111 for n>3 n=6: a(n) = (1/120)*n^5 + (3/8)*n^4 + (149/24)*n^3 + (2521/8)*n^2 + (56417/60)*n + 385 for n>4 n=7: a(n) = (1/120)*n^5 + (5/12)*n^4 + (187/24)*n^3 + (7393/12)*n^2 + (20667/10)*n + 1143 for n>5 EXAMPLE Some solutions for n=4 k=4 ..0....0....1....0....1....0....0....0....0....1....0....1....1....0....0....1 ..0....1....2....0....2....2....0....1....1....0....0....2....2....1....1....1 ..0....2....0....1....0....2....1....0....0....1....1....0....2....0....2....1 ..0....0....0....2....0....0....2....0....0....1....1....0....2....0....2....2 ..2....0....2....0....1....2....2....0....1....2....1....0....0....2....2....2 ..2....0....2....1....2....2....2....2....1....1....1....1....1....2....0....0 ..0....2....1....1....0....2....1....0....2....2....2....0....2....2....0....1 ..0....0....1....1....0....0....2....1....2....2....1....2....2....2....1....1 CROSSREFS Column 1 is A000244(n+1) Column 2 is A018919(n+1) Sequence in context: A144114 A209969 A144701 * A022421 A075395 A085367 Adjacent sequences:  A255104 A255105 A255106 * A255108 A255109 A255110 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Feb 14 2015 STATUS approved

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Last modified February 20 21:15 EST 2020. Contains 332084 sequences. (Running on oeis4.)