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).

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

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