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 A210603 Triangle of coefficients of polynomials u(n,x) jointly generated with A210738; see the Formula section. 3

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

%S 1,2,2,4,6,4,7,17,16,8,12,39,57,40,16,20,84,159,169,96,32,33,170,405,

%T 551,465,224,64,54,332,950,1608,1727,1217,512,128,88,630,2115,4264,

%U 5655,5055,3073,1152,256,143,1171,4515,10603,16666,18294,14079

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210738; see the Formula section.

%C Row n starts with F(n+2)-1, where F=A000045 (Fibonacci

%C numbers), and ends with 2^(n-1). For a discussion and

%C guide to related arrays, see A208510.

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

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

%e 4....6....4

%e 7....17...16...8

%e 12...39...57...40...16

%e First three polynomials u(n,x): 1, 2+ 2x, 4 + 6x + 4x^2.

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

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

%t v[n_, x_] := (x + 1)*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[%] (* A210603 *)

%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[%] (* A210738 *)

%Y Cf. A210738, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 24 2012

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Last modified September 19 14:36 EDT 2024. Contains 376012 sequences. (Running on oeis4.)