A234789 - OEIS

A234789

Number of (n+1) X (1+1) 0..3 arrays with each 2 X 2 subblock having the number of clockwise edge increases less than or equal to the number of counterclockwise edge increases.

204, 2504, 30536, 371976, 4530424, 55175944, 671983416, 8184025736, 99672501944, 1213902270984, 14784004509496, 180053035925896, 2192849421966264, 26706512126351624, 325256163423006776, 3961265003235768456

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OFFSET

1,1

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 15*a(n-1) - 36*a(n-2) + 20*a(n-3).

Conjectures from Colin Barker, Oct 16 2018: (Start)

G.f.: 4*x*(51 - 139*x + 80*x^2) / ((1 - 2*x)*(1 - 13*x + 10*x^2)).

a(n) = (1/129)*2^(-1-n)*(-129*2^(1+2*n) + (2193-191*sqrt(129))*(13-sqrt(129))^n + (13+sqrt(129))^n*(2193+191*sqrt(129))).

(End)

EXAMPLE

Some solutions for n=3:

..2..3....1..2....2..0....2..3....1..0....1..0....2..1....0..1....3..2....1..0

..2..3....0..1....2..0....3..1....3..2....3..2....0..2....0..1....2..0....2..0

..2..2....2..0....3..2....3..1....0..0....2..0....2..1....0..1....2..3....3..0

..0..0....1..3....2..0....0..0....1..1....2..3....2..0....2..3....3..3....1..3

CROSSREFS

Column 1 of A234796.

Sequence in context: A292346 A338153 A234796 * A099105 A253680 A209790

Adjacent sequences: A234786 A234787 A234788 * A234790 A234791 A234792

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 30 2013

STATUS

approved