OFFSET
0,1
COMMENTS
Terms are either 1, 3, or 7 mod 10.
Using the formula, we see that the cubes produced are (2^n+1)^3 for all n.
This is a particular case of general formula
(3 + 3 f + f^2) f + 1 = (1 + f)^3 with f = 2^n.
For the simplest case f = n, we have (3 + 3 n + n^2) = A002061 (Central polygonal numbers, with corresponding offset). - Zak Seidov, Mar 24 2014
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-14,8).
FORMULA
a(n) = 3 + 3*2^n + 2^(2*n).
G.f.: -(38*x^2-36*x+7) / ((x-1)*(2*x-1)*(4*x-1)). - Colin Barker, Mar 24 2014
EXAMPLE
13*(2^1)+1 = 27 is a cube. Since 13 is the smallest coefficient that returns a cube, then a(1) = 13.
PROG
(Python) {print(3+3*(2**n)+2**(2*n)) for n in range(100)}
(PARI) for(n=0, 100, k=1; while(!ispower(k*2^n+1, 3), k++); print1(k, ", ")) \\ Colin Barker, Mar 24 2014
(PARI) a(n) = (3+3*2^n+4^n) \\ Colin Barker, Mar 24 2014
(PARI) Vec(-(38*x^2-36*x+7)/((x-1)*(2*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Mar 24 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Derek Orr, Mar 23 2014
STATUS
approved