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A238731 Riordan array ((1-2*x)/(1-3*x+x^2), x/(1-3*x+x^2)).

%I A238731 #13 Jul 16 2019 09:53:05
%S A238731 1,1,1,2,4,1,5,13,7,1,13,40,33,10,1,34,120,132,62,13,1,89,354,483,308,
%T A238731 100,16,1,233,1031,1671,1345,595,147,19,1,610,2972,5561,5398,3030,
%U A238731 1020,203,22,1,1597,8495,17984,20410,13893,5943,1610,268,25,1,4181
%N A238731 Riordan array ((1-2*x)/(1-3*x+x^2), x/(1-3*x+x^2)).
%C A238731 Unsigned version of A124037 and A126126.
%C A238731 Subtriangle of the triangle given by (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C A238731 Row sums are A001075(n).
%C A238731 Diagonal sums are A133494(n).
%C A238731 Sum_{k=0..n} T(n,k)*x^k = A001519(n), A001075(n), A002320(n), A038723(n), A033889(n) for x = 0, 1, 2, 3, 4 respectively. - _Philippe Deléham_, Mar 05 2014
%F A238731 T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - T(n-2,k), T(0,0) = T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.
%F A238731 G.f.: (1-2*x)/(1-(y+3)*x+x^2). - _Philippe Deléham_, Mar 05 2014
%e A238731 Triangle begins:
%e A238731 1;
%e A238731 1, 1;
%e A238731 2, 4, 1;
%e A238731 5, 13, 7, 1;
%e A238731 13, 40, 33, 10, 1;
%e A238731 34, 120, 132, 62, 13, 1;
%e A238731 89, 354, 483, 308, 100, 16, 1;
%e A238731 233, 1031, 1671, 1345, 595, 147, 19, 1;...
%e A238731 Triangle (0, 1, 1, 1, 0, 0, 0, ...) DELTA (1, 0, 2, -2, 0, 0, ...) begins:
%e A238731 1;
%e A238731 0, 1;
%e A238731 0, 1, 1;
%e A238731 0, 2, 4, 1;
%e A238731 0, 5, 13, 7, 1;
%e A238731 0, 13, 40, 33, 10, 1;
%e A238731 0, 34, 120, 132, 62, 13, 1;
%e A238731 0, 89, 354, 483, 308, 100, 16, 1;
%e A238731 0, 233, 1031, 1671, 1345, 595, 147, 19, 1;...
%t A238731 (* The function RiordanArray is defined in A256893. *)
%t A238731 RiordanArray[(1-2#)/(1-3#+#^2)&, x/(1-3#+#^2)&, 10] // Flatten (* _Jean-François Alcover_, Jul 16 2019 *)
%Y A238731 Cf. A001519, A000012, A016777, A062708.
%Y A238731 Cf. A001906, A124037, A126126.
%K A238731 nonn,tabl
%O A238731 0,4
%A A238731 _Philippe Deléham_, Mar 03 2014