This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A230000 Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(k)*x^k which is the numerator of the n-th convergent of the continued fraction [1, 1/x, 1/x^2, ... ,1/x^n]. 13
 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 0, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 2, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,36 COMMENTS In the Name section, k = n(n+1)/2.  For the denominator polynomials, see A230001.  Conjecture:  every nonnegative integer occurs infinitely many times. LINKS FORMULA Write the numerator polynomials as u(0), u(1), u(2), ... and the denominator polynomials as v(0), v(1), v(2),...  Let p(0) = 1, q(0) = 1; p(1) = (1 + x)/x; q(1) = 1/x; p(n ) = p(n-1)/x^n + p(n-2), q(n) = q(n-1)/x^n + q(n-2).  Then u(n)/v(n) = p(n)/q(n) for n>=0. EXAMPLE The first 7 rows: 1 . . . . . . . . . . . . polynomial u(0) = 1 1 1 . . . . . . . . . . . polynomial u(1) = 1 + x 1 1 0 1 . . . . . . . . . u(2) = 1 + x + x^3 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 2 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 2 1 2 0 2 1 1 1 1 1 0 1 MATHEMATICA t[n_] := t[n] = Table[1/x^k, {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] CROSSREFS Cf. A230001. Sequence in context: A239366 A014944 A015879 * A016242 A216659 A321396 Adjacent sequences:  A229997 A229998 A229999 * A230001 A230002 A230003 KEYWORD nonn,tabf AUTHOR Clark Kimberling, Oct 11 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 12 05:15 EST 2018. Contains 318052 sequences. (Running on oeis4.)