login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A231154 Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^n which is the numerator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 1)/(x - 1). 1
1, 1, 2, 0, 2, 3, 1, 1, 3, 5, 0, 6, 0, 5, 8, 0, 8, 8, 0, 8, 13, -2, 19, 4, 19, -2, 13, 21, -5, 33, 15, 15, 33, -5, 21, 34, -12, 64, 12, 60, 12, 64, -12, 34, 55, -25, 116, 20, 90, 90, 20, 116, -25, 55, 89, -50, 213, 8, 210, 84, 210, 8, 213, -50, 89 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Sum of numbers in row n:  2^n.  Left and right edges:  A000045 (Fibonacci numbers).

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

First 5 rows:

1 . . . 1

2 . . . 0 . . . 2

3 . . . 1 . . . 1 . . . 3

5 . . . 0 . . . 6 . . . 0 . . . 5

8 . . . 0 . . . 8 . . . 8 . . . 0 . . . 8

First 3 polynomials:  1 + x, 2 + 2*x^2, 3 + x + x^2 + 3*x^3.

MATHEMATICA

t[n_] := t[n] = Table[(x + 1)/(x - 1), {k, 0, n}];

b = Table[Factor[Convergents[t[n]]], {n, 0, 10}];

p[x_, n_] := p[x, n] = Last[Expand[Numerator[b]]][[n]];

u = Table[p[x, n], {n, 1, 10}]

v = CoefficientList[u, x]; Flatten[v]

CROSSREFS

Cf. A230000, A000045, A231727.

Sequence in context: A114327 A330240 A330237 * A073450 A284592 A071447

Adjacent sequences:  A231151 A231152 A231153 * A231155 A231156 A231157

KEYWORD

sign,tabf

AUTHOR

Clark Kimberling, Nov 13 2013

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 May 11 13:41 EDT 2021. Contains 343791 sequences. (Running on oeis4.)