A176972 a(n) = 7^n + 7*n + 1.

2, 15, 64, 365, 2430, 16843, 117692, 823593, 5764858, 40353671, 282475320, 1977326821, 13841287286, 96889010499, 678223072948, 4747561510049, 33232930569714, 232630513987327, 1628413597910576, 11398895185373277, 79792266297612142, 558545864083284155, 3909821048582988204

Offset: 0

Author

Jonathan Vos Post, Apr 29 2010

Keywords

• easy
• nonn

Examples

			a(5) = 7^5 + 7*5 + 1 = 16843 is prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (9,-15,7).

Crossrefs

Cf. A000420, A008589, A016993, A176691, A176805, A176916.

Cf. A370664.

Programs

Magma

[7^n + 7*n + 1: n in [0..25]]; // Vincenzo Librandi, May 06 2011

Mathematica

Table[7^n+7n+1,{n,0,20}] (* or *) LinearRecurrence[{9,-15,7},{2,15,64},20] (* Harvey P. Dale, Apr 17 2014 *)

Formula

a(n) = A000420(n) + A008589(n) + 1 = A000420(n) + A016993(n).

a(n) = 7*a(n-1) - 42*(n-1) + 1, with n > 0. For n=5, a(5) = 7*2430 - 42*4 + 1 = 16843. - Bruno Berselli, May 18 2010

From R. J. Mathar, May 22 2010: (Start)

a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3).

G.f.: (-2 + 3*x + 41*x^2) / ((7*x-1)*(x-1)^2). (End)

E.g.f.: exp(x)*(1 + exp(6*x) + 7*x). - Stefano Spezia, Aug 19 2024