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A210187 Triangle of coefficients of polynomials u(n,x) jointly generated with A210188; see the Formula section.

%I A210187 #6 Mar 30 2012 18:58:16
%S A210187 1,3,6,2,10,9,2,15,25,13,2,21,55,49,17,2,28,105,140,81,21,2,36,182,
%T A210187 336,285,121,25,2,45,294,714,825,506,169,29,2,55,450,1386,2079,1716,
%U A210187 819,225,33,2,66,660,2508,4719,5005,3185,1240,289,37,2,78,935,4290
%N A210187 Triangle of coefficients of polynomials u(n,x) jointly generated with A210188; see the Formula section.
%C A210187 Row sums: even-indexed Fibonacci numbers: 1,3,8,21,55,...
%C A210187 Column 1:  triangular numbers: A000217
%C A210187 Alternating row sums:  periodic with period (1,3,4,3,1,0)
%C A210187 For a discussion and guide to related arrays, see A208510.
%F A210187 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210187 v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210187 where u(1,x)=1, v(1,x)=1.
%e A210187 First five rows:
%e A210187 1
%e A210187 3
%e A210187 6....2
%e A210187 10...9....2
%e A210187 15...25...13...2
%e A210187 First three polynomials u(n,x): 1, 3, 6 + 2x.
%t A210187 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210187 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210187 v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210187 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210187 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210187 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210187 TableForm[cu]
%t A210187 Flatten[%]    (* A210187 *)
%t A210187 Table[Expand[v[n, x]], {n, 1, z}]
%t A210187 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210187 TableForm[cv]
%t A210187 Flatten[%]    (* A210188 *)
%Y A210187 Cf. A210188, A208510.
%K A210187 nonn,tabf
%O A210187 1,2
%A A210187 _Clark Kimberling_, Mar 18 2012