A231733 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 denominator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 2)/(x + 1).

1, 1, 2, 3, 1, 5, 11, 8, 2, 12, 34, 36, 17, 3, 29, 101, 141, 99, 35, 5, 70, 289, 499, 462, 242, 68, 8, 169, 807, 1659, 1905, 1320, 552, 129, 13, 408, 2212, 5272, 7218, 6210, 3438, 1196, 239, 21, 985, 5977, 16198, 25738, 26427, 18183, 8383, 2497, 436, 34

Offset

1,3

Comments

Sum of numbers in row n: 2*A015521(n). Left edge: A000129. Right edge: A000045 (Fibonacci numbers).

Links

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

Example

First 3 rows:
1 ... 1
2 ... 3 ... 1
5 ... 11 .. 8 .. 2
First 3 polynomials:  1 + x, 2 + 3*x + x^2, 5 + 11*x + 8*x^2 + 2*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[Denominator[b]]][[n]];
u = Table[p[x, n], {n, 1, 10}]
v = CoefficientList[u, x]; Flatten[v]

Crossrefs

Cf. A230000, A231732.

Sequence in context: A147315 A085853 A185997 * A182822 A137211 A212275

Adjacent sequences: A231730 A231731 A231732 * A231734 A231735 A231736

Keyword

nonn,tabf

Author

Clark Kimberling, Nov 13 2013

Status

approved