Search: id:A099328
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%I A099328
%S A099328 1,0,1,0,2,2,8,8,21,28,69,108,226,370,736,1280,2473,4392,8281,14920,
%T A099328 27874,50706,94088,171880,317693,582116,1073853,1970836,3630914,6669730,
%U A099328 12279296,22568896,41533777,76360464,140493041,258344528,475256898
%N A099328 Number of Catalan knight paths from (0,0) to (n,0) in the region between 
               and on the lines y=0 and y=3. (See A096587 for the definition of 
               Catalan knight.).
%F A099328 Taking A099328 to A099331 as the rows of an array T, the recurrences 
               for these row sequences are given for n>=2 by T(n, 0) = T(n-1, 2) 
               + T(n-2, 1), T(n, 1) = T(n-1, 3) + T(n-2, 0) + T(n-2, 2), T(n, 2) 
               = T(n-1, 0) + T(n-2, 1) + T(n-2, 3), T(n, 3) = T(n-1, 1) + T(n-2, 
               2), with initial values T(0, 0)=1, T(1, 2)=1.
%e A099328 a(6) counts 8 paths from (0,0) to (6,0); the final move in 5 of the paths 
               is from the point (5,2) and the final move in the other 3 paths is 
               from (4,1).
%Y A099328 Cf. A099329, A099330, A099331.
%Y A099328 Sequence in context: A060818 A082887 A137583 this_sequence A073090 A120544 
               A155950
%Y A099328 Adjacent sequences: A099325 A099326 A099327 this_sequence A099329 A099330 
               A099331
%K A099328 nonn
%O A099328 1,5
%A A099328 Clark Kimberling (ck6(AT)evansville.edu), Oct 12 2004

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