A184038 1/16 the number of (n+1) X 9 0..3 arrays with all 2 X 2 subblocks having the same four values.

1225, 1237, 1258, 1300, 1378, 1534, 1834, 2434, 3610, 5962, 10618, 19930, 38458, 75514, 149434, 297274, 592570, 1183162, 2363578, 4724410, 9444538, 18884794, 37762234, 75517114, 151020730, 302027962, 604030138, 1208034490, 2416018618

Offset

1,1

Comments

Column 8 of A184039.

Links

R. H. Hardin, Table of n, a(n) for n = 1..53

Formula

Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).

Conjectures from Colin Barker, Apr 10 2018: (Start)

G.f.: x*(1225 - 2438*x - 2453*x^2 + 4876*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 1210 for n even.

a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 1210 for n odd.

(End)

Example

Some solutions for 3 X 9:
..3..0..3..1..3..0..3..1..3....0..0..3..1..3..1..0..0..0
..1..1..1..0..1..1..1..0..1....3..1..0..0..0..0..3..1..3
..3..0..3..1..3..0..3..1..3....0..0..3..1..3..1..0..0..0

Crossrefs

Sequence in context: A014488 A229379 A229371 * A025407 A025405 A275256

Adjacent sequences: A184035 A184036 A184037 * A184039 A184040 A184041

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved