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A236420 Riordan array (1/(1-3*x), (1-3*x-sqrt(1-6*x+5*x^2))/(2*x)).

%I A236420 #4 Jan 26 2014 00:34:21
%S A236420 1,3,1,9,6,1,27,28,9,1,81,120,56,12,1,243,497,300,93,15,1,729,2034,
%T A236420 1490,594,139,18,1,2187,8321,7098,3411,1029,194,21,1,6561,34248,33026,
%U A236420 18360,6692,1632,258,24,1,19683,142331,151686,94798,40068,11846,2430,331,27,1
%N A236420 Riordan array (1/(1-3*x), (1-3*x-sqrt(1-6*x+5*x^2))/(2*x)).
%C A236420 T(n,0) = 3^n = A000244(n).
%C A236420 T(n,2) = A002212(n+1) - 3^n.
%C A236420 T(n+1,n) = 3n+3 = A008585(n+1).
%C A236420 T(n+2,n) = (9*n^2+29*n+18)/2.
%F A236420 T(n,0) = 3*T(n-1,0), T(n,k) = T(n-1,k-1) + 3*T(n-1,k) + T(n-1,k+1) for k>0, T(n,k) = 0 if k<0 or if k>n, T(0,0) = 1.
%e A236420 Triangle begins:
%e A236420 1;
%e A236420 3, 1;
%e A236420 9, 6, 1;
%e A236420 27, 28, 9, 1;
%e A236420 81, 120, 56, 12, 1;
%e A236420 243, 497, 300, 93, 15, 1;
%e A236420 729, 2034, 1490, 594, 139, 18, 1
%Y A236420 Cf. Similar sequences: A091965, A110165
%K A236420 nonn,tabl
%O A236420 0,2
%A A236420 _Philippe Deléham_, Jan 25 2014