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, 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

Author

R. H. Hardin, Mar 22 2002

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-13,3,4).

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.

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

Extensions

An incorrect recurrence was deleted by N. J. A. Sloane, Sep 13 2009

More terms from Sean A. Irvine, Aug 23 2024