A208086 Number of 4 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.
24, 56, 134, 344, 888, 2318, 6056, 15848, 41478, 108584, 284264, 744206, 1948344, 5100824, 13354118, 34961528, 91530456, 239629838, 627359048, 1642447304, 4299982854, 11257501256, 29472520904, 77160061454, 202007663448
Offset: 1
Keywords
Examples
Some solutions for n=4: ..0..0..1..0..0....0..0..0..1..1....0..0..0..1..0....0..1..0..1..0 ..1..1..1..1..1....0..1..0..1..0....0..1..0..1..0....1..0..1..0..1 ..1..1..1..1..1....1..0..1..0..1....1..0..1..0..1....1..0..1..0..1 ..0..1..0..1..0....1..1..1..1..1....1..0..0..0..0....0..1..0..1..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A208085.
Formula
Empirical: a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4).
Conjectures from Colin Barker, Jun 27 2018: (Start)
G.f.: 2*x*(12 - 8*x - 17*x^2 + 7*x^3) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)).
a(n) = 2^(1-n)*(2^n*(15+2*(-1)^n) + (9-4*sqrt(5))*(3-sqrt(5))^n + (3+sqrt(5))^n*(9+4*sqrt(5))) / 5.
(End)
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