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A069361
Number of 3 X n binary arrays with a path of adjacent 1's from top row to bottom row.
94
1, 17, 197, 1985, 18621, 167337, 1461797, 12519345, 105683341, 882516857, 7308428597, 60131384705, 492202181661, 4012347269577, 32599584662597, 264152863210065, 2135714594033581, 17236446198921497, 138901692341235797, 1117982939085627425, 8989229069675479101
OFFSET
1,2
FORMULA
G.f.: x*(1+2*x)/((1-8*x)*(2*x^2-7*x+1)). - Vladeta Jovovic, Jul 02 2003
From Maksym Voznyy (voznyy(AT)mail.ru), Jul 25 2008: (Start)
a(n) = 15*a(n-1) - 58*a(n-2) + 16*a(n-3), where a(1)=1, a(2)=17, a(3)=197;
a(n) = 8^n + 1/sqrt(41)*4^(n+1)*((7+sqrt(41))^(-(n+1)) - (7-sqrt(41))^(-(n+1))). (End)
a(n) = 8^n - A186446(n). - R. J. Mathar, Jan 27 2020
EXAMPLE
The 17 binary arrays for n=2:
01 10 01 10 01 10 01 10 01 10 11 11 11 11 11 11 11
01 10 01 10 11 11 11 11 11 11 01 10 01 01 11 11 11
01 10 11 11 01 10 10 01 11 11 01 10 11 11 01 10 11 - R. J. Mathar, Jun 21 2023
MATHEMATICA
CoefficientList[Series[(-2 z - 1)/(16 z^3 - 58 z^2 + 15 z - 1), {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 24 2011 *)
PROG
(PARI) x='x+O('x^30); Vec(x*(1+2*x)/((1-8*x)*(2*x^2-7*x+1))) \\ G. C. Greubel, Apr 22 2018
CROSSREFS
Row 3 of A359576.
Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.
Sequence in context: A238672 A018250 A021184 * A177135 A130817 A055432
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Mar 22 2002
STATUS
approved