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A069361
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Number of 3 X n binary arrays with a path of adjacent 1's from top row to bottom row.
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92
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1, 17, 197, 1985, 18621, 167337, 1461797, 12519345, 105683341, 882516857, 7308428597, 60131384705, 492202181661, 4012347269577, 32599584662597, 264152863210065, 2135714594033581, 17236446198921497, 138901692341235797, 1117982939085627425, 8989229069675479101
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| G.f.: x*(1+2*x)/((1-8*x)*(2*x^2-7*x+1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 02 2003
Recurrence: a(n)=15*a(n-1)-58*a(n-2)+16*a(n-3), where a(1)=1, a(2)=17, a(3)=197; formula a(n)=8^n+1/sqrt(41)*4^(n+1)*((7+sqrt(41))^(-(n+1))-(7-sqrt(41))^(-(n+1))) - Maksym Voznyy (voznyy(AT)mail.ru), Jul 25 2008
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MATHEMATICA
| CoefficientList[Series[(-2 z - 1)/(16 z^3 - 58 z^2 + 15 z - 1), {z, 0, 100}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 24 2011 *)
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CROSSREFS
| 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: A019316 A018250 A021184 * A177135 A130817 A055432
Adjacent sequences: A069358 A069359 A069360 * A069362 A069363 A069364
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KEYWORD
| nonn
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net), Mar 22 2002.
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