A176805 a(n) = 3^n + 3*n + 1.

2, 7, 16, 37, 94, 259, 748, 2209, 6586, 19711, 59080, 177181, 531478, 1594363, 4783012, 14348953, 43046770, 129140215, 387420544, 1162261525, 3486784462, 10460353267, 31381059676, 94143178897, 282429536554, 847288609519, 2541865828408, 7625597485069, 22876792455046

Offset: 0

Author

Jonathan Vos Post, Apr 26 2010

Keywords

• easy
• nonn

Examples

			a(7) = (3^7) + (3*7) + 1 = 2209 = 47^2.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

Crossrefs

Cf. A000244, A008585, A016777, A176691.

Programs

Magma

[3^n + 3*n + 1: n in [0..30]]; // Vincenzo Librandi, May 09 2011

PARI

a(n)=3^n+3*n+1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 3^n + 3n + 1 = A000244(n) + A008585(n) + 1 = A000244(n) + A016777(n).

From R. J. Mathar, Apr 27 2010: (Start)

a(n)= 5*a(n-1) - 7*a(n-2) + 3*a(n-3).

G.f.: (1+x)*(5*x-2) / ( (3*x-1)*(x-1)^2 ). (End)

E.g.f.: exp(x)*(1 + exp(2*x) + 3*x). - Stefano Spezia, Aug 19 2024

Extensions

Corrected (1 replaced by 2, 2209 inserted) by R. J. Mathar, Apr 27 2010