A069307 Number of 3 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.
21, 110, 581, 3070, 16227, 85776, 453423, 2396868, 12670261, 66977242, 354053617, 1871590506, 9893561055, 52299127660, 276462513603, 1461430140016, 7725380293233, 40837737667414, 215875562691877
Offset: 2
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Formula
G.f.: x^2*(21-37*x+14*x^3-8*x^4)/(1+2*x^5-7*x+9*x^2+x^3-4*x^4). - Vladeta Jovovic, Jul 02 2003