A099359 a(n) = (2^n + 1)^3 - 2.

6, 25, 123, 727, 4911, 35935, 274623, 2146687, 16974591, 135005695, 1076890623, 8602523647, 68769820671, 549957165055, 4398851866623, 35187593412607, 281487861809151, 2251851353686015, 18014604668698623, 144116012711149567, 1152924803144876031

Offset: 0

Author

Parthasarathy Nambi, Nov 16 2004

Keywords

• nonn
• easy

Examples

			(2^1 + 1)^3 - 2 = 25.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Integer sequence primes.
• Index entries for linear recurrences with constant coefficients, signature (15,-70,120,-64).

Crossrefs

Cf. A098878.

Programs

Mathematica

Table[(2^n + 1)^3 - 2, {n, 19}] (* Robert G. Wilson v, Nov 23 2004 *)

PARI

a(n)=(2^n+1)^3-2 \\ Charles R Greathouse IV, Feb 19 2016

PARI

Vec((6 - 65*x + 168*x^2 - 88*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 8*x)) + O(x^30)) \\ Colin Barker, Jan 10 2017

Formula

From Colin Barker, Jan 10 2017: (Start)

a(n) = (3*2^n + 3*4^n + 8^n - 1).

a(n) = 15*a(n-1) - 70*a(n-2) + 120*a(n-3) - 64*a(n-4) for n>3.

G.f.: (6 - 65*x + 168*x^2 - 88*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 8*x)).

(End)

Extensions

More terms from Robert G. Wilson v, Nov 23 2004