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A213221 Riordan array (f(x), x*g(x)) where f(x) is the g.f. of A157004 and g(x) is the g.f. of A157003.

%I A213221 #15 Aug 08 2015 10:32:56
%S A213221 1,2,1,6,3,1,18,10,4,1,58,32,15,5,1,192,106,52,21,6,1,650,357,180,79,
%T A213221 28,7,1,2232,1222,624,288,114,36,8,1,7746,4230,2178,1035,439,158,45,9,
%U A213221 1,27096,14770,7648,3706,1642,643,212,55,10,1
%N A213221 Riordan array (f(x), x*g(x)) where f(x) is the g.f. of A157004 and g(x) is the g.f. of A157003.
%D A213221 Baccherini, D.; Merlini, D.; Sprugnoli, R. Binary words excluding a pattern and proper Riordan arrays. Discrete Math. 307 (2007), no. 9-10, 1021--1037. MR2292531 (2008a:05003). See page 1032. - _N. J. A. Sloane_, Mar 25 2014
%F A213221 Column k has g.f. ((1-sqrt(1-4*x+4*x^3))/(2*(1-x^2)))^k/sqrt(1-4*x+4*x^3).
%F A213221 T(n,0) = 2*T(n,1) - 2*T(n-2,1), T(n+1,k+1) = T(n,k) + T(n+1,k+2) - T(n-1,k+2) for n>=0.
%e A213221 Triangle begins
%e A213221 1
%e A213221 2, 1
%e A213221 6, 3, 1
%e A213221 18, 10, 4, 1
%e A213221 58, 32, 15, 5, 1
%e A213221 192, 106, 52, 21, 6, 1
%e A213221 650, 357, 180, 79, 28, 7, 1
%e A213221 2232, 1222, 624, 288, 114, 36, 8, 1
%e A213221 7746, 4230, 2178, 1035, 439, 158, 45, 9, 1
%e A213221 27096, 14770, 7648, 3706, 1642, 643, 212, 55, 10, 1
%e A213221 95376, 51918, 27000, 13265, 6056, 2508, 911, 277, 66, 11, 1
%e A213221 337404, 183472, 95744, 47532, 22174, 9552, 3708, 1255, 354, 78, 12, 1
%Y A213221 Cf. A157003, A157004 (column k=0), A261058 (column k=1).
%K A213221 nonn,tabl
%O A213221 0,2
%A A213221 _Philippe Deléham_, Mar 02 2013