A259221 Number of (n+1) X (7+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
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
Examples
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
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 7 of A259222.
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