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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210211 Triangle of coefficients of polynomials u(n,x) jointly generated with A210212; see the Formula section. 3
1, 2, 1, 3, 4, 1, 4, 8, 8, 1, 5, 14, 19, 16, 1, 6, 21, 42, 42, 32, 1, 7, 30, 72, 114, 89, 64, 1, 8, 40, 120, 216, 290, 184, 128, 1, 9, 52, 178, 414, 593, 706, 375, 256, 1, 10, 65, 260, 670, 1292, 1531, 1666, 758, 512, 1, 11, 80, 355, 1090, 2247, 3754, 3782 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with n and ends with 2^n followed by 1.

n-th row sum: F(2k), where F=A000045 (Fibonacci numbers)

Alternating row sums are signed products of two Fibonacci numbers.

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

LINKS

Table of n, a(n) for n=1..62.

FORMULA

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

2...1

3...4....1

4...8....8....1

5...14...19...16...1

First three polynomials u(n,x): 1, 2 + x, 3 + 4x + x^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_] := 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[%]    (* A210211 *)

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

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

TableForm[cv]

Flatten[%]    (* A210212 *)

CROSSREFS

Cf. A210204, A208510.

Sequence in context: A180378 A208341 A201634 * A283054 A247358 A297224

Adjacent sequences:  A210208 A210209 A210210 * A210212 A210213 A210214

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 19 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 19 21:01 EDT 2019. Contains 328225 sequences. (Running on oeis4.)