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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210549 Triangle of coefficients of polynomials u(n,x) jointly generated with A210550; see the Formula section. 2
1, 1, 2, 1, 3, 4, 1, 3, 9, 8, 1, 3, 10, 25, 16, 1, 3, 10, 33, 65, 32, 1, 3, 10, 34, 104, 161, 64, 1, 3, 10, 34, 115, 311, 385, 128, 1, 3, 10, 34, 116, 381, 886, 897, 256, 1, 3, 10, 34, 116, 395, 1224, 2421, 2049, 512, 1, 3, 10, 34, 116, 396, 1334, 3796, 6388 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Each row begins with 1 and ends with 2^(n-1).

Row sums: 1,3,8,21,..., the even-indexed Fibonacci numbers

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

LINKS

Table of n, a(n) for n=1..64.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...2

1...3...4

1...3...9....8

1...3...10...25...16

First three polynomials u(n,x): 1, 1 + 2x, 1 + 3x + 4x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*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[%]      (* A210235 *)

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

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

TableForm[cv]

Flatten[%]      (* A210236 *)

CROSSREFS

Cf. A210550, A208510.

Sequence in context: A027422 A135086 A210561 * A187002 A177226 A059026

Adjacent sequences:  A210546 A210547 A210548 * A210550 A210551 A210552

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 22 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 October 20 12:47 EDT 2019. Contains 328257 sequences. (Running on oeis4.)