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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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

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

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

EXAMPLE

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

PROG

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

CROSSREFS

Column 1 of A263060.

Cf. A052992.

Sequence in context: A216708 A032005 A147801 * A066965 A066966 A132443

Adjacent sequences:  A263050 A263051 A263052 * A263054 A263055 A263056

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 08 2015

STATUS

approved

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Last modified September 26 20:26 EDT 2022. Contains 357032 sequences. (Running on oeis4.)