cp's OEIS Frontend

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).

%I A231733 #5 Nov 02 2014 12:18:36
%S A231733 1,1,2,3,1,5,11,8,2,12,34,36,17,3,29,101,141,99,35,5,70,289,499,462,
%T A231733 242,68,8,169,807,1659,1905,1320,552,129,13,408,2212,5272,7218,6210,
%U A231733 3438,1196,239,21,985,5977,16198,25738,26427,18183,8383,2497,436,34
%N 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).
%C A231733 Sum of numbers in row n:  2*A015521(n).  Left edge:  A000129.  Right edge:  A000045 (Fibonacci numbers).
%e A231733 First 3 rows:
%e A231733 1 ... 1
%e A231733 2 ... 3 ... 1
%e A231733 5 ... 11 .. 8 .. 2
%e A231733 First 3 polynomials:  1 + x, 2 + 3*x + x^2, 5 + 11*x + 8*x^2 + 2*x^3.
%t A231733 t[n_] := t[n] = Table[(x + 2)/(x + 1), {k, 0, n}];
%t A231733 b = Table[Factor[Convergents[t[n]]], {n, 0, 10}];
%t A231733 p[x_, n_] := p[x, n] = Last[Expand[Denominator[b]]][[n]];
%t A231733 u = Table[p[x, n], {n, 1, 10}]
%t A231733 v = CoefficientList[u, x]; Flatten[v]
%Y A231733 Cf. A230000, A231732.
%K A231733 nonn,tabf
%O A231733 1,3
%A A231733 _Clark Kimberling_, Nov 13 2013