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A210878 Triangle of coefficients of polynomials u(n,x) jointly generated with A210879; see the Formula section. 3

%I

%S 1,0,3,0,4,7,0,2,14,17,0,2,12,46,41,0,2,8,54,140,99,0,2,8,42,212,408,

%T 239,0,2,8,34,200,758,1154,577,0,2,8,34,160,866,2544,3194,1393,0,2,8,

%U 34,144,754,3448,8154,8696,3363,0,2,8,34,144,642,3400,12850

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210879; see the Formula section.

%C Leading coefficient of u(n,x): A001333

%C Limiting row: 0,2,8,34,144,610,...(Fibonacci numbers)

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

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

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

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

%e First six rows:

%e 1

%e 0...3

%e 0...4...7

%e 0...2...14...17

%e 0...2...12...46...41

%e 0...2...8....54...140...99

%e First three polynomials u(n,x): 1, 3x, 4x + 7x^2.

%t u[1, x_] := 1; v[1, x_] := 1; z = 14;

%t u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x];

%t v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 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[%] (* A210878 *)

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

%t TableForm[cv]

%t Flatten[%] (* A210879 *)

%Y Cf. A210879, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 30 2012

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Last modified January 18 13:47 EST 2020. Contains 331009 sequences. (Running on oeis4.)