OFFSET
0,2
COMMENTS
For any n > 0, the equation y^2 = x^3 - a(n) has exactly one solution in natural numbers (x = 12*n^2 and y = 36*n^3).
LINKS
Arkadiusz Wesolowski, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
G.f.: 432*x*(1 + x)*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6. - Colin Barker, Dec 11 2017
EXAMPLE
a(2) = 432*2^6 = 27648.
MAPLE
seq(432*n^6, n=0..22);
MATHEMATICA
Table[432*n^6, {n, 0, 22}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 432, 27648, 314928, 1769472, 6750000, 20155392}, 40] (* Harvey P. Dale, Apr 06 2018 *)
PROG
(Magma) [432*n^6 : n in [0..22]];
(PARI) concat(0, Vec(432*x*(1 + x)*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1 - x)^7 + O(x^40))) \\ Colin Barker, Dec 11 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Arkadiusz Wesolowski, Aug 10 2013
STATUS
approved