A231731 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 = 2*x + 1.

1, 2, 2, 4, 4, 3, 10, 12, 8, 5, 20, 36, 32, 16, 8, 40, 88, 112, 80, 32, 13, 76, 204, 320, 320, 192, 64, 21, 142, 444, 840, 1040, 864, 448, 128, 34, 260, 932, 2048, 3040, 3136, 2240, 1024, 256, 55, 470, 1896, 4752, 8176, 10080, 8960, 5632, 2304, 512, 89, 840

Offset: 1

Author

Clark Kimberling, Nov 13 2013

Keywords

• nonn
• tabf

Comments

Sum of numbers in row n: A006190(n). Left edge: A000045 (Fibonacci numbers). Right edge: powers of 2

Examples

			First 3 rows:
1 ... 2
2 ... 4 .... 4
3 ... 10 ... 12 ... 8
First 3 polynomials:  1 + 2*x, 2 + 4*x + 4*x^2, 3 + 10*x + 12*x^2 + 8*x^3.
		

Crossrefs

Cf. A230000, A231730.

Programs

Mathematica

t[n_] := t[n] = Table[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]