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
Examples
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.
Programs
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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]
Comments