The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A177893

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A177893

Irregular triangle read by rows giving coefficients of Yablonskii-Vorob'ev polynomials.
(history; published version)

#26 by Andrey Zabolotskiy at Tue Mar 19 20:01:15 EDT 2024

STATUS

editing

approved

#25 by Andrey Zabolotskiy at Tue Mar 19 20:01:10 EDT 2024

COMMENTS

From Table 1, p.2 of Roffelsen. The Yablonskii-Vorob'ev polynomials are defined by the equation Q_(n+1)*Q_(n-1) = z*(Q_n)^2 - 4*(Q_n * (Q_n)'' - ((Q_n)')^2, ), with Q_0 = 1 and Q_1 = z.

STATUS

approved

editing

#24 by Bruno Berselli at Wed Sep 29 10:54:50 EDT 2021

STATUS

reviewed

approved

#23 by Joerg Arndt at Wed Sep 29 08:58:14 EDT 2021

STATUS

proposed

reviewed

#22 by Andrey Zabolotskiy at Wed Sep 29 08:48:15 EDT 2021

STATUS

editing

proposed

#21 by Andrey Zabolotskiy at Wed Sep 29 08:44:31 EDT 2021

MATHEMATICA

a[f_, n_] := Module[{t, = {{1}}, p, = 1, q, = 1, z},

t = {{1}};

p = q = 1;

t];

];

#20 by Andrey Zabolotskiy at Wed Sep 29 08:28:05 EDT 2021

MATHEMATICA

Flatten[Reverse[#][[; ; ; ; 3]]& /@ a[1, 6][[; ; , -1; ; 1; ; -3]]] (* A092766 *)

#19 by Andrey Zabolotskiy at Wed Sep 29 08:25:22 EDT 2021

MATHEMATICA

r[q_, f_, z_] := z q^2 + f (q D[q, z, z] - D[q, z]^2);

t = {{1}};

p = q = 1;

Do[{p, q} = {q, Simplify[r[q, -4]/p]}; AppendTo[t, CoefficientList[q, z]], 6];

Flatten@t (* this sequence *)

a[f_, n_] := Module[{t, p, q, z},

Do[{p, q} = {q, Simplify[r[q, 1f, z]/p]}; AppendTo[t, Reverse[CoefficientList[q, z]][[; ; ; ; 3]]], 6, n];

t

];

Flatten[a[-4, 6]] (* this sequence *)

Flatten[Reverse[#][[; ; ; ; 3]]& /@t a[1, 6]] (* A092766 *)

STATUS

proposed

editing

#18 by Michel Marcus at Wed Sep 29 08:22:14 EDT 2021

STATUS

editing

proposed

Discussion

Wed Sep 29

08:23

Andrey Zabolotskiy: Yes, thanks.

#17 by Michel Marcus at Wed Sep 29 08:21:01 EDT 2021

COMMENTS

From Table 1, p.2 of Roffelsen. The Yablonskii-Vorob'ev polynomials are defined by the equation Q_(n+1)*Q_(n-1) = z*(Q_n)^2 - 4*(Q_n * (Q_n)'' - ((Q_n)')^2, with Q_0 = 1 and Q_1 = z.

are defined by the equation

Q_(n+1)*Q_(n-1) = z*(Q_n)^2 - 4*(Q_n * (Q_n)'' - ((Q_n)')^2, with Q_0 = 1 and Q_1 = z

STATUS

proposed

editing

Discussion

Wed Sep 29

08:22

Michel Marcus: ok ?