OFFSET
0,2
REFERENCES
L. Lorentzen and H. Waadeland, Continued Fractions with Applications, North-Holland 1992, p. 562.
E. Maor, e: The Story of a Number, Princeton Univ. Press 1994, pp. 151 and 157.
M. A. Stern, Theorie der Kettenbrüche und ihre Anwendung, Crelle, 1832, pp. 1-22.
LINKS
Leonhardo Eulero, Introductio in analysin infinitorum. Tomus primus, Lausanne, 1748.
L. Euler, Introduction à l'analyse infinitésimale, Tome premier, Tome second, trad. du latin en français par J. B. Labey, Paris, 1796-1797.
EXAMPLE
Convergents are 1, 5/3, 23/15, 45/29, 925/597, 7285/4701, ...
MAPLE
for j from 1 to 50 do printf(`%d, `, numer(cfrac([1, seq([i, i+1], i=2..j)]))); od:
MATHEMATICA
num[0]=1; num[1]=5; num[n_] := num[n] = (n+2)*num[n-1] + (n+1)*num[n-2]; den[0]=1; den[1]=3; den[n_] := den[n] = (n+2)*den[n-1] + (n+1)*den[n-2]; a[n_] := Numerator[num[n]/den[n]]; Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Jan 16 2013 *)
CROSSREFS
KEYWORD
nonn,frac,nice,easy
AUTHOR
N. J. A. Sloane, Jan 15 2000
EXTENSIONS
More terms from James A. Sellers, Feb 02 2000
STATUS
approved