A259220 Number of (n+1) X (6+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

162, 230, 334, 510, 798, 1278, 2078, 3422, 5694, 9566, 16222, 27774, 48030, 83934, 148286, 264926, 478686, 874622, 1615390, 3014238, 5678142, 10789470, 20661854, 39839870, 77278878, 150673118, 295060798, 579951582, 1143447774, 2260270206

Offset: 1

Author

R. H. Hardin, Jun 21 2015

Keywords

• nonn
• easy

Examples

			Some solutions for n=4:
  0 1 0 1 0 1 0        0 1 1 1 0 1 1        1 1 0 0 1 1 1
  0 1 0 1 0 1 0        1 0 0 0 1 0 0        0 0 1 1 0 0 0
  0 1 0 1 0 1 0        1 0 0 0 1 0 0        1 1 0 0 1 1 1
  0 1 0 1 0 1 0        0 1 1 1 0 1 1        0 0 1 1 0 0 0
  1 0 1 0 1 0 1        1 0 0 0 1 0 0        1 1 0 0 1 1 1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (4,-4,-1,2).

Crossrefs

Column 6 of A259222.

Formula

a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).

G.f.: 2*x*(81 - 209*x + 31*x^2 + 128*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Dec 24 2018

From the above formulae, a(n) = 2*(2^n + 16*Fibonacci(n+3) + 31). - Ehren Metcalfe, Dec 27 2018