A231730 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 + 1/2.

1, 2, 5, 4, 4, 9, 22, 12, 8, 29, 56, 72, 32, 16, 65, 202, 232, 208, 80, 32, 181, 556, 924, 800, 560, 192, 64, 441, 1726, 2964, 3480, 2480, 1440, 448, 128, 1165, 4832, 10112, 12608, 11680, 7168, 3584, 1024, 256, 2929, 14066, 31632, 46752, 46816, 36288, 19712

Offset

1,2

Comments

Sum of numbers in row n: A015521(n). Left edge: A006131. Right edge: powers of 2

Links

Table of n, a(n) for n=1..51.

Example

First 3 rows:
1 .... 2
5 .... 4 .... 4
9 .... 22 ... 12 ... 8
First 3 polynomials:  1 + 2*x, 5 + 4*x + 4*x^2, 9 + 22*x + 12*x^2 + 8*x^3.

Mathematica

t[n_] := t[n] = Table[x + 1/2, {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, A231731.

Sequence in context: A325941 A104658 A335566 * A095758 A299212 A249018

Adjacent sequences: A231727 A231728 A231729 * A231731 A231732 A231733

Keyword

nonn,tabf

Author

Clark Kimberling, Nov 13 2013

Status

approved