A231727 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 + 1)/(x - 1).

-1, 1, -1, 0, 1, -2, 2, -2, 2, -3, 2, 0, -2, 3, -5, 5, -6, 6, -5, 5, -8, 8, -8, 0, 8, -8, 8, -13, 15, -21, 15, -15, 21, -15, 13, -21, 26, -38, 18, 0, -18, 38, -26, 21, -34, 46, -76, 52, -48, 48, -52, 76, -46, 34, -55, 80, -141, 96, -70, 0, 70, -96, 141, -80

Offset

1,6

Comments

Sum of numbers in row n: 0. Left and right edges: A000045 (Fibonacci numbers).

Links

Table of n, a(n) for n=1..64.

Example

First 5 rows:
-1 . . . 1
-1 . . . 0 . . . 1
-2 . . . 2 . . . -2 . . . 2
-3 . . . 2 . . . 0 . . . -2 . . . 3
-5 . . . 5 . . . -6 . . . 6 . . . -5 . . . 5
First 3 polynomials:  -1 + x, -1 + x^2, -2 + 2*x - 2*x^2 + 2*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[Denominator[b]]][[n]];
u = Table[p[x, n], {n, 1, 10}]
v = CoefficientList[u, x]; Flatten[v]

Crossrefs

Cf. A230000, A000045, A231154.

Sequence in context: A350959 A157372 A270559 * A368876 A270616 A304523

Adjacent sequences: A231724 A231725 A231726 * A231728 A231729 A231730

Keyword

sign,tabf

Author

Clark Kimberling, Nov 13 2013

Status

approved