cp's OEIS Frontend

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.

%I A069440 #27 Aug 23 2024 21:09:38
%S A069440 0,2,16,88,414,1810,7616,31376,127710,516170,2077552,8341288,33440190,
%T A069440 133941922,536205056,2145876128,8586053694,34350369050,137416333936,
%U A069440 549701205496,2198891419230,8795774741170,35183603690432,140735633277488,562945474867230
%N 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.
%H A069440 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-13,3,4).
%F A069440 From _Colin Barker_, May 22 2012: (Start)
%F A069440 a(n) = 7*a(n-1) - 13*a(n-2) + 3*a(n-3) + 4*a(n-4).
%F A069440 G.f.: 2*x^2*(1+x+x^2)/((1-x)*(1-4*x)*(1-2*x-x^2)). (End)
%F A069440 a(n) = 2^(2*n-1) - A001333(n+1) + 1. - _Sean A. Irvine_, Aug 23 2024
%Y A069440 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.
%K A069440 nonn,easy
%O A069440 1,2
%A A069440 _R. H. Hardin_, Mar 22 2002
%E A069440 An incorrect recurrence was deleted by _N. J. A. Sloane_, Sep 13 2009
%E A069440 More terms from _Sean A. Irvine_, Aug 23 2024