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A269619
T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.
12
2, 3, 4, 4, 9, 8, 5, 16, 27, 15, 6, 25, 64, 78, 28, 7, 36, 125, 249, 222, 51, 8, 49, 216, 612, 954, 624, 92, 9, 64, 343, 1275, 2956, 3611, 1740, 164, 10, 81, 512, 2370, 7440, 14125, 13544, 4824, 290, 11, 100, 729, 4053, 16218, 43013, 66925, 50442, 13320, 509, 12, 121
OFFSET
1,1
COMMENTS
Table starts
...2.....3......4.......5........6.........7.........8..........9.........10
...4.....9.....16......25.......36........49........64.........81........100
...8....27.....64.....125......216.......343.......512........729.......1000
..15....78....249.....612.....1275......2370......4053.......6504.......9927
..28...222....954....2956.....7440.....16218.....31822......57624......97956
..51...624...3611...14125....43013....110099....248143.....507521.....961625
..92..1740..13544...66925...246798....742487...1923796....4447329....9398090
.164..4824..50442..314935..1407232...4979260..14840928...38800210...91490344
.290.13320.186822.1473779..7982022..33232924.113998742..337209090..887591878
.509.36672.688899.6865098.45074673.220896016.872397577.2920747321.8584628259
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3)
k=3: a(n) = 12*a(n-1) -51*a(n-2) +81*a(n-3) -3*a(n-4) -63*a(n-5) -24*a(n-6) -9*a(n-7)
k=4: [order 7]
k=5: [order 13]
k=6: [order 15]
k=7: [order 17]
Empirical for row n:
n=1: a(n) = n + 1
n=2: a(n) = n^2 + 2*n + 1
n=3: a(n) = n^3 + 3*n^2 + 3*n + 1
n=4: a(n) = n^4 + 4*n^3 + 5*n^2 + 5*n
n=5: a(n) = n^5 + 5*n^4 + 7*n^3 + 12*n^2 + 3*n
n=6: a(n) = n^6 + 6*n^5 + 9*n^4 + 22*n^3 + 9*n^2 + 9*n - 7 for n>2
n=7: a(n) = n^7 + 7*n^6 + 11*n^5 + 35*n^4 + 18*n^3 + 36*n^2 - 19*n - 7 for n>2
EXAMPLE
Some solutions for n=6 k=4
..1. .2. .0. .2. .1. .4. .3. .4. .2. .2. .0. .2. .2. .2. .2. .0
..0. .3. .3. .1. .4. .0. .0. .0. .2. .1. .0. .1. .0. .2. .4. .3
..4. .3. .2. .1. .1. .3. .0. .4. .1. .0. .4. .3. .1. .2. .4. .1
..3. .3. .2. .2. .4. .2. .4. .0. .3. .3. .0. .3. .4. .3. .3. .1
..0. .3. .1. .3. .0. .1. .3. .4. .1. .1. .2. .1. .4. .1. .4. .1
..0. .3. .0. .4. .4. .1. .4. .2. .1. .0. .1. .0. .3. .4. .2. .2
CROSSREFS
Column 1 is A029907(n+1).
Row 1 is A000027(n+1).
Row 2 is A000290(n+1).
Row 3 is A000578(n+1).
Sequence in context: A269690 A269494 A269776 * A269435 A269656 A223949
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 01 2016
STATUS
approved