OFFSET
1,1
COMMENTS
From Lewis Mammel (l_mammel(AT)att.net), Aug 21 2008: (Start)
In Ramanujan's parametric equation: (ax+y)^3 + (b+x^2y)^3 = (bx+y)^3 + (a+x^2y)^3
where a^2 + ab + b^2 = 3xy^2.
This sequence is obtained by setting a=0, y=1 and finding the solution to b^2=3x:
b=3n, x=3n^2. (End)
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Tito Piezas III and Eric Weisstein, Diophantine Equation--3rd Powers [Lewis Mammel (l_mammel(AT)att.net), Aug 21 2008]
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 9*n^4 + 3*n, with b(n) = 9*n^4 and c(n) = 9*n^3 + 1 we have 1 + a(n)^3 = b(n)^3 + c(n)^3.
From Colin Barker, Oct 25 2019: (Start)
G.f.: 6*x*(2 + 15*x + 18*x^2 + x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
a(n) = 3*(n + 3*n^4).
(End)
EXAMPLE
For a(1)=12: 1 + 12^3 = 9^3 + 10^3 = 1729.
PROG
(PARI) Vec(6*x*(2 + 15*x + 18*x^2 + x^3) / (1 - x)^5 + O(x^40)) \\ Colin Barker, Oct 26 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Lewis Mammel (l_mammel(AT)att.net), Aug 03 2008
EXTENSIONS
Edited by Joerg Arndt, Oct 26 2019
STATUS
approved