A229586 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
0, 1, 0, 2, 6, 0, 6, 28, 40, 0, 16, 116, 264, 224, 0, 40, 444, 1620, 2160, 1152, 0, 96, 1620, 9156, 19764, 16416, 5632, 0, 224, 5724, 49848, 167364, 224532, 119232, 26624, 0, 512, 19764, 264300, 1375152, 2865780, 2440692, 839808, 122880, 0, 1152, 67068, 1374048
Offset: 1
Examples
Some solutions for n=3, k=4: 0 1 2 1 0 0 1 2 0 1 2 0 0 1 0 1 0 1 2 0 0 1 2 0 1 2 0 2 0 2 1 2 0 2 0 0 0 0 2 0 1 0 2 0 0 2 0 1 1 2 1 0 0 1 2 0 2 0 2 0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..287
Crossrefs
Row 1 is A057711(n-1).
Formula
Empirical for column k:
k=1: a(n) = a(n-1).
k=2: a(n) = 8*a(n-1) - 16*a(n-2) for n > 3.
k=3: a(n) = 12*a(n-1) - 36*a(n-2).
k=4: a(n) = 18*a(n-1) - 81*a(n-2) for n > 3.
k=5: a(n) = 30*a(n-1) - 261*a(n-2) + 540*a(n-3) - 324*a(n-4).
k=6: a(n) = 50*a(n-1) - 805*a(n-2) + 4662*a(n-3) - 12150*a(n-4) + 14580*a(n-5) - 6561*a(n-6).
k=7: [order 8]
Empirical for row n:
n=1: a(n) = 4*a(n-1) - 4*a(n-2) for n > 4.
n=2: a(n) = 6*a(n-1) - 9*a(n-2) for n > 4.
n=3: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4) for n > 6.
n=4: [order 6] for n > 12.
n=5: [order 14] for n > 18.
n=6: [order 18] for n > 26.
n=7: [order 54] for n > 60.
Comments