cp's OEIS Frontend

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.

%I A231731 #5 Nov 02 2014 12:18:36
%S A231731 1,2,2,4,4,3,10,12,8,5,20,36,32,16,8,40,88,112,80,32,13,76,204,320,
%T A231731 320,192,64,21,142,444,840,1040,864,448,128,34,260,932,2048,3040,3136,
%U A231731 2240,1024,256,55,470,1896,4752,8176,10080,8960,5632,2304,512,89,840
%N 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.
%C A231731 Sum of numbers in row n:  A006190(n).  Left edge:  A000045 (Fibonacci numbers).  Right edge:  powers of 2
%e A231731 First 3 rows:
%e A231731 1 ... 2
%e A231731 2 ... 4 .... 4
%e A231731 3 ... 10 ... 12 ... 8
%e A231731 First 3 polynomials:  1 + 2*x, 2 + 4*x + 4*x^2, 3 + 10*x + 12*x^2 + 8*x^3.
%t A231731 t[n_] := t[n] = Table[2 x + 1, {k, 0, n}];
%t A231731 b = Table[Factor[Convergents[t[n]]], {n, 0, 10}];
%t A231731 p[x_, n_] := p[x, n] = Last[Expand[Numerator[b]]][[n]];
%t A231731 u = Table[p[x, n], {n, 1, 10}]
%t A231731 v = CoefficientList[u, x]; Flatten[v]
%Y A231731 Cf. A230000, A231730.
%K A231731 nonn,tabf
%O A231731 1,2
%A A231731 _Clark Kimberling_, Nov 13 2013