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A209774 Triangle of coefficients of polynomials v(n,x) jointly generated with A209773; see the Formula section.

%I A209774 #5 Mar 30 2012 18:58:15
%S A209774 1,2,3,2,7,8,3,12,25,21,3,19,56,84,55,4,26,103,227,269,144,4,36,169,
%T A209774 486,848,833,377,5,45,259,914,2078,2999,2518,987,5,58,372,1565,4393,
%U A209774 8277,10192,7475,2584,6,69,518,2503,8342,19420,31269,33600,21881
%N A209774 Triangle of coefficients of polynomials v(n,x) jointly generated with A209773; see the Formula section.
%C A209774 Last term in row n: F(2n), where F=A000045, the Fibonacci numbers
%C A209774 For a discussion and guide to related arrays, see A208510.
%F A209774 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209774 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A209774 where u(1,x)=1, v(1,x)=1.
%e A209774 First five rows:
%e A209774 1
%e A209774 2...3
%e A209774 2...7....8
%e A209774 3...12...25...21
%e A209774 3...19...56...84...55
%e A209774 First three polynomials v(n,x): 1, 2 + 3x , 2 + 7x + 8x^2.
%t A209774 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209774 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209774 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209774 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209774 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209774 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209774 TableForm[cu]
%t A209774 Flatten[%]    (* A209773 *)
%t A209774 Table[Expand[v[n, x]], {n, 1, z}]
%t A209774 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209774 TableForm[cv]
%t A209774 Flatten[%]    (* A209774 *)
%Y A209774 Cf. A209673, A208510.
%K A209774 nonn,tabl
%O A209774 1,2
%A A209774 _Clark Kimberling_, Mar 15 2012