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A239101 Riordan array read by rows, corresponding to array in A180562.

%I A239101 #20 Sep 15 2014 04:04:06
%S A239101 1,2,1,4,2,1,10,5,2,1,26,13,6,2,1,70,35,16,7,2,1,192,96,45,19,8,2,1,
%T A239101 534,267,126,56,22,9,2,1,1500,750,357,160,68,25,10,2,1,4246,2123,1016,
%U A239101 463,198,81,28,11,2,1,12092,6046,2907,1337,586,240,95,31
%N A239101 Riordan array read by rows, corresponding to array in A180562.
%C A239101 Take lower triangle of square array in A180562, read from right to left.
%C A239101 Row sums are in A225034. - _Philippe Deléham_, Mar 25 2014
%C A239101 Riordan array (f(x), (f(x)-1)/(2*f(x))) where f(x) = sqrt((1+x)/(1-3*x)). - _Philippe Deléham_, Mar 25 2014
%H A239101 D. Baccherini, D. Merlini, R. Sprugnoli, <a href="http://dx.doi.org/10.1016/j.disc.2006.07.023">Binary words excluding a pattern and proper Riordan arrays</a>, Discrete Math. 307 (2007), no. 9-10, 1021--1037. MR2292531 (2008a:05003).
%F A239101 T(0,0) = 1, T(n,0) = 2*T(n,1) for n>0, T(n,k) = T(n-1,k-1) - T(n-1,k) + T(n-1,k+1) + T(n,k+1) for k>0, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Mar 25 2014
%e A239101 Triangle begins:
%e A239101 1
%e A239101 2 1
%e A239101 4 2 1
%e A239101 10 5 2 1
%e A239101 26 13 6 2 1
%e A239101 70 35 16 7 2 1
%e A239101 192 96 45 19 8 2 1
%e A239101 ...
%e A239101 192 = 2*96, 96 = 70 - 35 + 16 + 45, 45 = 35 - 16 + 7 + 19, etc. - _Philippe Deléham_, Mar 25 2014
%e A239101 Production matrix is:
%e A239101 2, 1
%e A239101 0, 0, 1
%e A239101 2, 1, 0, 1
%e A239101 2, 1, 1, 0, 1
%e A239101 2, 1, 1, 1, 0, 1
%e A239101 2, 1, 1, 1, 1, 0, 1
%e A239101 2, 1, 1, 1, 1, 1, 0, 1
%e A239101 2, 1, 1, 1, 1, 1, 1, 0, 1
%e A239101 ... _Philippe Deléham_, Sep 15 2014
%Y A239101 Cf. A180562.
%Y A239101 Cf. T(n,0) = A025565(n+1), T(n+1,1) = A005773(n+1), T(n+2,2) = A005717(n+1), A225034 (Row sums). - _Philippe Deléham_, Mar 25 2014
%K A239101 nonn,tabl,more
%O A239101 0,2
%A A239101 _N. J. A. Sloane_, Mar 25 2014
%E A239101 More terms from _Philippe Deléham_, Mar 25 2014