A206170 Number of 2 X (n+1) 0..3 arrays with every 2 X 2 subblock in a row having an equal number of equal diagonal or equal antidiagonal elements, adjacent rows differing in this number, and new values 0..3 introduced in row major order.

15, 85, 641, 5257, 44585, 385465, 3375401, 29817817, 264999305, 2364834745, 21162573161, 189737549977, 1703284356425, 15303437762425, 137574211418921, 1237227532571737, 11129405572871945, 100130796836040505

Offset

1,1

Comments

Row 1 of A206169.

Links

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

Formula

Empirical: a(n) = 18*a(n-1) - 101*a(n-2) + 192*a(n-3) - 108*a(n-4).

Conjectures from Colin Barker, Mar 04 2018: (Start)

G.f.: x*(15 - 185*x + 626*x^2 - 576*x^3) / ((1 - x)*(1 - 2*x)*(1 - 6*x)*(1 - 9*x)).

a(n) = (9 + 3*2^n + 2^(1+n)*3^n + 2*9^n) / 3.

(End)

Example

Some solutions for n=4:
..0..0..1..0..2....0..0..0..0..1....0..0..0..1..2....0..1..2..3..2
..3..2..1..3..3....1..1..1..2..1....0..1..0..0..1....3..1..2..1..0

Crossrefs

Cf. A206169.

Sequence in context: A160747 A064058 A138322 * A177882 A199897 A367228

Adjacent sequences: A206167 A206168 A206169 * A206171 A206172 A206173

Keyword

nonn

Author

R. H. Hardin, Feb 04 2012

Status

approved