login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210564 Triangle of coefficients of polynomials v(n,x) jointly generated with A210563; see the Formula section. 3
1, 2, 3, 2, 7, 8, 2, 8, 22, 21, 2, 8, 29, 67, 55, 2, 8, 30, 101, 200, 144, 2, 8, 30, 111, 341, 588, 377, 2, 8, 30, 112, 404, 1122, 1708, 987, 2, 8, 30, 112, 417, 1442, 3613, 4913, 2584, 2, 8, 30, 112, 418, 1543, 5044, 11425, 14018, 6765, 2, 8, 30, 112, 418 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Last terms in rows: even-indexed Fibonacci numbers

Limiting row:  A052530

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

LINKS

Table of n, a(n) for n=1..60.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...3

2...7...8

2...8...22...21

2...8...29...67...55

First three polynomials v(n,x): 1, 2 + 3x , 2 + 8x + 22x^2.

MATHEMATICA

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

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

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

Table[Expand[u[n, x]], {n, 1, z/2}]

Table[Expand[v[n, x]], {n, 1, z/2}]

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]  (* A210563 *)

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

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

TableForm[cv]

Flatten[%]  (* A210564 *)

CROSSREFS

Cf. A210563, A208510.

Sequence in context: A256581 A122697 A129022 * A208930 A122076 A209774

Adjacent sequences:  A210561 A210562 A210563 * A210565 A210566 A210567

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 23 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 20 22:20 EDT 2019. Contains 327252 sequences. (Running on oeis4.)