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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
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 A352775
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 14 2015
STATUS
approved

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Last modified May 17 19:53 EDT 2024. Contains 372607 sequences. (Running on oeis4.)