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Riordan array ((1-3x+x^2)/(1-4x+3x^2), x(1-2x)/(1-4x+3x^2)).
4

%I #11 Jul 19 2019 11:47:58

%S 1,1,1,2,3,1,5,9,5,1,14,28,20,7,1,41,89,75,35,9,1,122,285,273,154,54,

%T 11,1,365,913,974,634,273,77,13,1,1094,2918,3420,2502,1256,440,104,15,

%U 1,3281,9297,11850,9578,5439,2239,663,135,17,1

%N Riordan array ((1-3x+x^2)/(1-4x+3x^2), x(1-2x)/(1-4x+3x^2)).

%C Triangle [1,1,1,1,0,0,0,....] DELTA [1,0,0,0,....] with DELTA as in A084938.

%C Row sums are A147748. A147747=A147746*A007318.

%F T(n,k) = 4*T(n-1,k) + T(n-1,k-1) - 3*T(n-2,k) - 2*T(n-2,k-1), T(0,0) = T(0,1) = T(1,1) = T(2,2) = 1, T(2,0) = 2, T(2,1) = 3, T(n,k) = 0 if k>n or if k<0. - _Philippe Deléham_, Oct 29 2013

%F G.f.: (1 - 3*x + x^2)/(1 - 4*x + 3*x^2 - x*y + 2*x^2*y). - _Philippe Deléham_, Oct 29 2013

%e Triangle begins

%e 1,

%e 1, 1,

%e 2, 3, 1,

%e 5, 9, 5, 1,

%e 14, 28, 20, 7, 1,

%e 41, 89, 75, 35, 9, 1,

%e 122, 285, 273, 154, 54, 11, 1

%t (* The function RiordanArray is defined in A256893. *)

%t RiordanArray[(1-3#+#^2)/(1-4#+3#^2)&, # (1-2#)/(1-4#+3#^2)&, 10] // Flatten (* _Jean-François Alcover_, Jul 19 2019 *)

%K easy,nonn,tabl

%O 0,4

%A _Paul Barry_, Nov 11 2008