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 A209771 Triangle of coefficients of polynomials u(n,x) jointly generated with A209772; see the Formula section. 3

%I

%S 1,1,2,2,5,4,2,9,14,8,3,14,32,36,16,3,20,60,100,88,32,4,27,100,220,

%T 288,208,64,4,35,154,420,728,784,480,128,5,44,224,728,1568,2240,2048,

%U 1088,256,5,54,312,1176,3024,5376,6528,5184,2432,512,6,65,420

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209772; 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+1)*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 five rows:

%e 1

%e 1...2

%e 2...5....4

%e 2...9....14...8

%e 3...14...32...36...16

%e First three polynomials u(n,x): 1, 1 + 2x, 2 + 5x + 4x^2.

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

%t u[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%] (* A209771 *)

%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[%] (* A209772 *)

%Y Cf. A209772, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 15 2012

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Last modified January 29 17:53 EST 2023. Contains 359925 sequences. (Running on oeis4.)