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A210806 Triangle of coefficients of polynomials v(n,x) jointly generated with A210805; see the Formula section. 4

%I #5 Mar 30 2012 18:58:17

%S 1,0,2,1,1,3,0,3,3,5,1,2,8,7,8,0,4,8,19,15,13,1,3,15,25,42,30,21,0,5,

%T 15,46,67,89,58,34,1,4,24,58,128,164,182,109,55,0,6,24,90,186,330,378,

%U 363,201,89,1,5,35,110,300,536,804,833,709,365,144,0,7,35,155

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210805; see the Formula section.

%C Row n ends with F(n), where F=A000045 (Fibonacci numbers).

%C Column 1: 1,0,1,0,1,0,1,0,...

%C Alternating row sums: signed Fibonacci numbers.

%C For a discussion and guide to related arrays, see A208510.

%F u(n,x)=u(n-1,x)+x*v(n-1,x),

%F v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x)-1,

%F where u(1,x)=1, v(1,x)=1.

%e First five rows:

%e 1

%e 0...2

%e 1...1...3

%e 0...3...3...5

%e 1...2...8...7...8

%e First three polynomials v(n,x): 1, 2x, 1 + x + 3x^2

%t u[1, x_] := 1; v[1, x_] := 1; z = 16;

%t u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;

%t d[x_] := h + x; e[x_] := p + x;

%t v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;

%t j = 0; c = 0; h = 2; p = -1; f = -1;

%t Table[Expand[u[n, x]], {n, 1, z/2}]

%t Table[Expand[v[n, x]], {n, 1, z/2}]

%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

%t TableForm[cu]

%t Flatten[%] (* A210805 *)

%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

%t TableForm[cv]

%t Flatten[%] (* A210806 *)

%Y Cf. A210805, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 27 2012

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Last modified April 17 12:12 EDT 2024. Contains 371763 sequences. (Running on oeis4.)