A269678 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo k+1.
2, 3, 4, 4, 9, 6, 5, 16, 24, 10, 6, 25, 60, 66, 14, 7, 36, 120, 224, 174, 22, 8, 49, 210, 570, 820, 462, 30, 9, 64, 336, 1212, 2670, 2976, 1206, 46, 10, 81, 504, 2282, 6918, 12390, 10700, 3150, 62, 11, 100, 720, 3936, 15358, 39156, 57030, 38224, 8166, 94, 12, 121
Offset: 1
Examples
Some solutions for n=6 k=4 ..0. .1. .4. .0. .2. .4. .0. .4. .4. .4. .4. .4. .3. .0. .4. .4 ..2. .3. .2. .3. .3. .1. .0. .2. .4. .2. .0. .3. .3. .3. .0. .2 ..0. .2. .4. .2. .4. .3. .4. .1. .0. .3. .3. .2. .0. .0. .3. .3 ..3. .3. .1. .1. .1. .4. .1. .2. .2. .3. .2. .1. .4. .4. .3. .4 ..0. .3. .3. .0. .4. .2. .0. .3. .0. .2. .1. .0. .3. .4. .4. .1 ..1. .2. .4. .2. .4. .2. .4. .1. .4. .0. .2. .1. .4. .3. .2. .3
Links
- R. H. Hardin, Table of n, a(n) for n = 1..9999
Crossrefs
Formula
Empirical for column k:
k=1: a(n) = a(n-1) +2*a(n-2) -2*a(n-3)
k=2: a(n) = 3*a(n-1) +2*a(n-2) -8*a(n-3)
k=3: a(n) = 5*a(n-1) -a(n-2) -15*a(n-3)
k=4: a(n) = 7*a(n-1) -6*a(n-2) -24*a(n-3)
k=5: a(n) = 9*a(n-1) -13*a(n-2) -35*a(n-3)
k=6: a(n) = 11*a(n-1) -22*a(n-2) -48*a(n-3)
k=7: a(n) = 13*a(n-1) -33*a(n-2) -63*a(n-3)
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 + 2 for n>1
n=5: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 + 4*n - 2 for n>1
n=6: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 + 6*n^2 + 6 for n>1
n=7: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 + 8*n^3 + 10*n^2 + 12*n - 10 for n>1
Comments