A269035 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
0, 3, 0, 12, 24, 0, 36, 48, 120, 0, 96, 216, 348, 504, 0, 240, 672, 2166, 2136, 1944, 0, 576, 2208, 9528, 18384, 12228, 7128, 0, 1344, 6912, 44760, 115656, 146064, 67104, 25272, 0, 3072, 21408, 198816, 785124, 1326576, 1114848, 357756, 87480, 0, 6912, 65280
Offset: 1
Examples
Some solutions for n=4 k=4 ..2..1..0..0. .0..0..1..0. .0..1..0..1. .2..0..0..1. .2..2..2..1 ..0..1..0..0. .0..1..0..0. .0..0..0..1. .0..1..0..1. .1..2..2..2 ..2..1..0..1. .0..1..0..0. .2..1..0..1. .2..1..0..1. .2..2..2..2 ..0..0..0..0. .0..1..0..1. .0..1..0..1. .0..1..0..0. .1..1..2..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..337
Formula
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 6*a(n-1) -9*a(n-2) for n>3
k=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>5
k=4: a(n) = 14*a(n-1) -57*a(n-2) +56*a(n-3) -16*a(n-4) for n>5
k=5: [order 12] for n>13
k=6: [order 18] for n>19
k=7: [order 38] for n>39
Empirical for row n:
n=1: a(n) = 4*a(n-1) -4*a(n-2)
n=2: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4)
n=3: a(n) = 6*a(n-1) -a(n-2) -28*a(n-3) -4*a(n-4) +16*a(n-5) -4*a(n-6) for n>8
n=4: [order 12] for n>14
n=5: [order 20] for n>22
n=6: [order 46] for n>48
n=7: [order 92] for n>94
Comments