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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210752 Triangle of coefficients of polynomials v(n,x) jointly generated with A210751; see the Formula section. 3
1, 2, 3, 3, 8, 8, 4, 15, 27, 21, 5, 24, 61, 86, 55, 6, 35, 114, 227, 265, 144, 7, 48, 190, 484, 799, 798, 377, 8, 63, 293, 905, 1910, 2703, 2362, 987, 9, 80, 427, 1546, 3951, 7150, 8874, 6898, 2584, 10, 99, 596, 2471, 7391, 16188, 25711, 28455, 19929 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with n and ends with F(2n), where F=A000045 (Fibonacci numbers).

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

LINKS

Table of n, a(n) for n=1..54.

FORMULA

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

3...8....8

4...15...27...21

5...24...61...86...55

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

MATHEMATICA

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

u[n_, x_] := (x + 1)*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[%]    (* A210751 *)

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

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

TableForm[cv]

Flatten[%]    (* A210752 *)

CROSSREFS

Cf. A210751, A208510.

Sequence in context: A202818 A256679 A193997 * A210599 A211879 A308774

Adjacent sequences:  A210749 A210750 A210751 * A210753 A210754 A210755

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 25 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 22 03:04 EDT 2019. Contains 328315 sequences. (Running on oeis4.)