OFFSET
1,1
COMMENTS
All numbers in this sequence are divisible by 4.
All polynomials are symmetric and reducible in rationals extended by 5^(1/2) and 5^(1/4).
REFERENCES
Computed by Michael Trott.
LINKS
M. Trott, Modular Equations of the Rogers-Ramanujan Continued Fraction, The Mathematica Journal, 9:2, 314-333, 2004.
Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction
EXAMPLE
R(e^(-Pi))=Root[1-14*#1+22*#1^2-22*#1^3+30*#1^4+22*#1^5+22*#1^6+14*#1^7+#1^8&,4], so a(1)=8.
R(e^(-2*Pi))=Root[1-2*#1-6*#1^2+2*#1^3+#1^4&,3], so a(2)=4.
MATHEMATICA
(* Program not suitable to compute more than a few terms *)
terms = 12; prec = 3000; QP = QPochhammer;
R[q_] := q^(1/5)*QP[q, q^5]*QP[q^4, q^5]/(QP[q^2, q^5]*QP[q^3, q^5]);
a[n_] := N[R[E^(-n Pi)], prec] // RootApproximant // MinimalPolynomial[#, x]& // Exponent[#, x]&;
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, terms}] (* Jean-François Alcover, Dec 22 2017 *)
CROSSREFS
KEYWORD
nonn,more,nice
AUTHOR
Eric W. Weisstein, Apr 10 2003
EXTENSIONS
a(11)-a(21) computed by Artur Jasinski, Aug 24 2016
STATUS
approved