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A069440
Half the number of n X 2 binary arrays with no path of adjacent 1's or adjacent 0's from top row to bottom row.
0
0, 2, 16, 88, 414, 1810, 7616, 31376, 127710, 516170, 2077552, 8341288, 33440190, 133941922, 536205056, 2145876128, 8586053694, 34350369050, 137416333936, 549701205496, 2198891419230, 8795774741170, 35183603690432, 140735633277488, 562945474867230
OFFSET
1,2
FORMULA
From Colin Barker, May 22 2012: (Start)
a(n) = 7*a(n-1) - 13*a(n-2) + 3*a(n-3) + 4*a(n-4).
G.f.: 2*x^2*(1+x+x^2)/((1-x)*(1-4*x)*(1-2*x-x^2)). (End)
a(n) = 2^(2*n-1) - A001333(n+1) + 1. - Sean A. Irvine, Aug 23 2024
CROSSREFS
Cf. 2 X n A000079, n X 1 A000225, 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: A071893 A220505 A370192 * A000431 A281982 A207595
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Mar 22 2002
EXTENSIONS
An incorrect recurrence was deleted by N. J. A. Sloane, Sep 13 2009
More terms from Sean A. Irvine, Aug 23 2024
STATUS
approved