A263053 Number of (n+1) X 2 0..1 arrays with each row and column not divisible by 3, read as a binary number with top and left being the most significant bits.

2, 2, 10, 10, 42, 42, 170, 170, 682, 682, 2730, 2730, 10922, 10922, 43690, 43690, 174762, 174762, 699050, 699050, 2796202, 2796202, 11184810, 11184810, 44739242, 44739242, 178956970, 178956970, 715827882, 715827882, 2863311530, 2863311530

Offset: 1

Author

R. H. Hardin, Oct 08 2015

Keywords

• nonn

Comments

Each row must be either 01 or 10. The two columns are therefore binary complements with sum 2^k-1, where k = n + 1 is the number of rows. If k is even then 2^k-1 is divisible by 3 and the number of solutions is 2*(2^k-1)/3. If k is odd then 2^k-1 == 1 (mod 3) and the number of solutions is (2^k-2)/3. - Andrew Howroyd, Feb 03 2022

Examples

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

Links

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

Crossrefs

Column 1 of A263060.

Cf. A052992.

Programs

Python

[int(2**n - 2/3 -((-2)**n)/3) for n in range(1,40)] # Pascal Bisson, Feb 03 2022

Formula

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

From Colin Barker, Jan 01 2019: (Start)

G.f.: 2*x / ((1 - x)*(1 - 2*x)*(1 + 2*x)).

a(n) = 2^n - 2/3 - (-2)^n/3.

(End)

a(n) = 2*A052992(n). - Pascal Bisson, Feb 03 2022