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A259221
Number of (n+1) X (7+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
2
311, 421, 588, 869, 1325, 2078, 3319, 5377, 8804, 14545, 24225, 40670, 68843, 117557, 202636, 352813, 620837, 1104574, 1987407, 3616121, 6651956, 12365081, 23211193, 43964734, 83952995, 161472013, 312533724, 608223317, 1189192349, 2334286430
OFFSET
1,1
FORMULA
a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).
G.f.: x*(311 - 823*x + 148*x^2 + 512*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Dec 24 2018
From the above formulae, a(n) = 2^(n+1) + 53*Fibonacci(n+3) + 148. - Ehren Metcalfe, Dec 27 2018
EXAMPLE
Some solutions for n=4:
1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 1 1
1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0
0 1 0 1 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 1
1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0
0 1 0 1 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 1
CROSSREFS
Column 7 of A259222.
Sequence in context: A059225 A157717 A113155 * A142626 A142950 A323050
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Jun 21 2015
STATUS
approved