%I A085810
%S A085810 1,2,5,13,35,96,266,741,2070,5791,16213,45409,127206,356384,998509,
%T A085810 2797678,7838801,21963661,61540563,172432468,483144522,1353740121,
%U A085810 3793094450,10628012915,29779028189
%N A085810 Number of three-choice paths along a corridor of width 6, starting from 
               one side.
%C A085810 Narrower corridors produce A000012, A000079, A000129, A001519, A057960. 
               An infinitely wide corridor would produce A005773.
%C A085810 Diagonal sums of A114164. - Paul Barry (pbarry(AT)wit.ie), Nov 15 2005
%D A085810 Roman Witula, Damian Slota and Adam Warzynski, Quasi-Fibonacci Numbers 
               of the Seventh Order, Journal of Integer Sequences, Vol. 9 (2006), 
               Article 06.4.3.
%F A085810 a(n) = 4*a(n-1) - 3*a(n-2) - a(n-3);
%F A085810 G.f.: (1-2x)/(1-4x+3x^2+x^3); a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, 
               C(n-k, j)C(j+k, 2k)}}; a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(n-k, 
               k+j)*C(k, k-j)2^(n-2k-j)}}; a(n)=sum{k=0..floor(n/2), sum{j=0..n-2k, 
               C(n-j, n-2k-j)C(k, j)(-1)^j*2^(n-2k-j)}}; - Paul Barry (pbarry(AT)wit.ie), 
               Nov 15 2005
%Y A085810 Cf. A000012 A000079 A000129 A001519 A057960 A005773.
%Y A085810 Sequence in context: A007075 A000107 A063028 this_sequence A005773 A022855 
               A091190
%Y A085810 Adjacent sequences: A085807 A085808 A085809 this_sequence A085811 A085812 
               A085813
%K A085810 easy,nonn
%O A085810 0,2
%A A085810 DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jul 25 2003