A184039 T(n,k) = 1/16 the number of (n+1) X (k+1) 0..3 arrays with all 2 X 2 subblocks having the same four values.
16, 28, 28, 49, 40, 49, 91, 61, 61, 91, 169, 103, 82, 103, 169, 325, 181, 124, 124, 181, 325, 625, 337, 202, 166, 202, 337, 625, 1225, 637, 358, 244, 244, 358, 637, 1225, 2401, 1237, 658, 400, 322, 400, 658, 1237, 2401, 4753, 2413, 1258, 700, 478, 478, 700, 1258
Offset: 1
Examples
Some solutions for 4X3 ..0..3..0....3..2..3....3..2..3....1..0..1....2..3..2....3..2..2....3..1..3 ..3..2..3....3..3..3....1..3..1....2..1..2....3..2..3....2..1..3....1..2..1 ..3..0..3....3..2..3....3..2..3....0..1..0....2..3..2....3..2..2....3..1..3 ..2..3..2....3..3..3....1..3..1....1..2..1....2..3..2....2..1..3....2..1..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..287
Crossrefs
Programs
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PARI
T(n,k) = my(m=4, b=t->2^t-1); m^2 + (m-1)^2*(b(n-1) + b(k-1)) + (m-1)*(b((n-1)\2) + b(n\2) + b((k-1)\2) + b(k\2)) \\ Andrew Howroyd, Mar 09 2024
Formula
Empirical, for all rows and columns: a(n)=3*a(n-1)-6*a(n-3)+4*a(n-4).
From Andrew Howroyd, Mar 09 2024: (Start)
The above empirical formula is correct.
T(n,k) = -14 + 9*(2^(n-1) + 2^(k-1)) + 3*(2^(floor((n-1)/2)) + 2^(floor(n/2)) + 2^(floor((k-1)/2)) + 2^(floor(k/2))). (End)
Comments