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A269537
T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than one.
12
2, 3, 4, 4, 9, 6, 5, 16, 24, 10, 6, 25, 60, 64, 14, 7, 36, 120, 222, 164, 22, 8, 49, 210, 568, 804, 418, 30, 9, 64, 336, 1210, 2648, 2878, 1048, 46, 10, 81, 504, 2280, 6890, 12214, 10192, 2614, 62, 11, 100, 720, 3934, 15324, 38878, 55836, 35812, 6468, 94, 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
..6....24.....60.....120......210.......336.......504........720........990
.10....64....222.....568.....1210......2280......3934.......6352.......9738
.14...164....804....2648.....6890.....15324.....30464......55664......95238
.22...418...2878...12214....38878....102202....234358.....485038.....926854
.30..1048..10192...55836...217714....677200...1792788....4205812....8981446
.46..2614..35812..253418..1211476...4462414..13648124...36313762...86704348
.62..6468.125012.1143256..6705102..29265308.103462888..312366672..834223586
.94.15942.434110.5131592.36939610.191134204.781425950.2678039200.8002547722
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +2*a(n-2) -2*a(n-3)
k=2: a(n) = 4*a(n-1) -a(n-2) -10*a(n-3) +6*a(n-4) +4*a(n-5)
k=3: a(n) = 7*a(n-1) -9*a(n-2) -23*a(n-3) +31*a(n-4) +33*a(n-5)
k=4: a(n) = 14*a(n-1) -65*a(n-2) +80*a(n-3) +163*a(n-4) -280*a(n-5) -208*a(n-6)
k=5: [order 7]
k=6: [order 9]
k=7: [order 9]
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 + 2*n
n=4: a(n) = n^4 + 4*n^3 + 3*n^2 + 2*n
n=5: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 - 2*n
n=6: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 - 6*n^2 + 6*n - 2
n=7: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 - 12*n^3 + 22*n^2 - 18*n + 4
EXAMPLE
Some solutions for n=6 k=4
..2. .4. .4. .0. .3. .0. .0. .3. .1. .2. .2. .3. .2. .1. .4. .0
..4. .3. .1. .3. .2. .2. .3. .0. .2. .0. .1. .0. .1. .3. .0. .2
..3. .2. .0. .1. .1. .4. .1. .0. .3. .3. .3. .1. .3. .0. .4. .2
..2. .1. .1. .2. .1. .0. .3. .2. .3. .4. .1. .0. .4. .2. .1. .4
..0. .3. .1. .2. .0. .1. .1. .4. .2. .1. .1. .1. .1. .4. .1. .0
..2. .1. .2. .4. .2. .1. .2. .0. .0. .2. .2. .2. .3. .2. .4. .4
CROSSREFS
Column 1 is A027383.
Row 1 is A000027(n+1).
Row 2 is A000290(n+1).
Row 3 is A007531(n+2).
Sequence in context: A269640 A269409 A268944 * A269678 A269467 A228461
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 29 2016
STATUS
approved