cp's OEIS Frontend

A231728 Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(2n)*x^(2n) which is the numerator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x^2 + 1)/(x + 1).

%I A231728 #9 May 14 2017 12:01:43
%S A231728 1,0,1,2,2,3,0,1,3,4,7,4,5,0,1,5,10,19,16,16,6,7,0,1,8,20,42,48,55,36,
%T A231728 29,8,9,0,1,13,40,94,132,164,138,119,64,46,10,11,0,1,21,76,197,324,
%U A231728 451,464,439,304,219,100,67,12,13,0,1,34,142,405,760,1170
%N A231728 Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(2n)*x^(2n) which is the numerator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x^2 + 1)/(x + 1).
%C A231728 Sum of numbers in row n:  2*A087206(n).  Left edge:  A000045 (Fibonacci numbers).
%e A231728 First 3 rows:
%e A231728 1 . . . 0 . . . 1
%e A231728 2 . . . 2 . . . 3 . . . 0 . . . 1
%e A231728 3 . . . 4 . . . 7 . . . 4 . . . 5 . . . 0 . . . 1
%e A231728 First 3 polynomials:  1 + x^2, 2 + 2*x + 3*x^2 + x^4.
%t A231728 t[n_] := t[n] = Table[(1 + x^2)/(1 + x), {k, 0, n}];
%t A231728 b = Table[Factor[Convergents[t[n]]], {n, 0, 10}];
%t A231728 p[x_, n_] := p[x, n] = Last[Expand[Numerator[b]]][[n]];
%t A231728 u = Table[p[x, n], {n, 1, 10}]
%t A231728 v = CoefficientList[u, x]; Flatten[v]
%Y A231728 Cf. A230000, A000045, A231729.
%K A231728 nonn,tabf
%O A231728 1,4
%A A231728 _Clark Kimberling_, Nov 13 2013