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 A209697 Triangle of coefficients of polynomials u(n,x) jointly generated with A209698; see the Formula section. 3

%I #5 Mar 30 2012 18:58:15

%S 1,0,2,0,2,4,0,3,6,8,0,4,10,16,16,0,5,15,30,40,32,0,6,21,50,84,96,64,

%T 0,7,28,77,154,224,224,128,0,8,36,112,258,448,576,512,256,0,9,45,156,

%U 405,810,1248,1440,1152,512,0,10,55,210,605,1362,2420,3360,3520

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209698; see the Formula section.

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

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

%F v(n,x)=x*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 0...2....4

%e 0...3....6...8

%e 0...4...10...16...16

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

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

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

%t v[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%] (* A209697 *)

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

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

%t TableForm[cv]

%t Flatten[%] (* A209698 *)

%Y Cf. A209698, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 12 2012

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Last modified June 14 15:00 EDT 2024. Contains 373400 sequences. (Running on oeis4.)