login
A183627
Number of (n+1) X 5 0..2 arrays with every 2 x 2 subblock summing to 4.
1
309, 447, 741, 1383, 2829, 6207, 14421, 35223, 89949, 238767, 654501, 1840263, 5274669, 15332127, 45012981, 133072503, 395284989, 1177990287, 3518241861, 10523267943, 31506888909, 94394837247, 282932853141, 848295242583
OFFSET
1,1
COMMENTS
Column 4 of A183632.
FORMULA
Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3).
Conjectures from Colin Barker, Mar 30 2018: (Start)
G.f.: 3*x*(103 - 469*x + 486*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).
a(n) = 3*(60 + 5*2^(2+n) + 3^n).
(End)
Formula and conjectures confirmed by Robert Israel, Mar 30 2018 (see link).
EXAMPLE
Some solutions for 3 X 5:
2 1 2 0 2 0 2 1 2 1 1 1 0 2 0 2 0 1 2 0
1 0 1 1 1 2 0 1 0 1 1 1 2 0 2 0 2 1 0 2
1 2 1 1 1 0 2 1 2 1 1 1 0 2 0 2 0 1 2 0
MAPLE
seq(3*(60 + 5*2^(2+n) + 3^n), n=1..30); # Robert Israel, Mar 30 2018
CROSSREFS
Cf. A183632.
Sequence in context: A061881 A121322 A067730 * A184544 A251345 A105841
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 06 2011
STATUS
approved