A228105 a(n) = 432*n^6.

0, 432, 27648, 314928, 1769472, 6750000, 20155392, 50824368, 113246208, 229582512, 432000000, 765314352, 1289945088, 2085181488, 3252759552, 4920750000, 7247757312, 10427429808, 14693280768, 20323820592, 27648000000, 37050964272, 48980118528

Offset: 0

Author

Arkadiusz Wesolowski, Aug 10 2013

Keywords

• nonn
• easy

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).

Examples

			a(2) = 432*2^6 = 27648.
		

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).

Crossrefs

Cf. A134109.

Programs

Magma

[432*n^6 : n in [0..22]];

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 *)

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

Formula

a(n) = A008585(n)*A008591(n)*A016744(n).

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