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A231732 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 + 2)/(x + 1). 1
2, 1, 5, 6, 2, 12, 22, 14, 3, 29, 72, 69, 30, 5, 70, 219, 280, 182, 60, 8, 169, 638, 1021, 884, 436, 116, 13, 408, 1804, 3468, 3750, 2460, 978, 218, 21, 985, 4992, 11206, 14532, 11895, 6288, 2095, 402, 34, 2378, 13589, 34888, 52760, 51750, 34119, 15112, 4334 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sum of numbers in row n:  A015521(n).  Left edge:  A000129.  Right edge:  A000045 (Fibonacci numbers).

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

First 3 rows:

2 .... 1

5 .... 6 .... 2

12 ... 22 ... 14 ... 3

First 3 polynomials:  2 + x, 5 + 6*x + 2*x^2, 12 + 22*x + 14*x^2 + 3*x^3.

MATHEMATICA

t[n_] := t[n] = Table[(x + 2)/(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, A231733.

Sequence in context: A323312 A231774 A209170 * A185384 A274728 A062991

Adjacent sequences:  A231729 A231730 A231731 * A231733 A231734 A231735

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Nov 13 2013

STATUS

approved

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Last modified September 25 11:39 EDT 2021. Contains 347654 sequences. (Running on oeis4.)