A094618 a(n) = 3^(n+1) - 2^(n+1) + n + 1.

2, 7, 22, 69, 216, 671, 2066, 6313, 19180, 58035, 175110, 527357, 1586144, 4766599, 14316154, 42981201, 129009108, 387158363, 1161737198, 3485735845, 10458256072, 31376865327, 94134790242, 282412759289, 847255055036, 2541798719491, 7625463267286, 22876524019533

Offset: 0

Author

Clark Kimberling, May 14 2004

Keywords

• nonn
• easy

Comments

Row sums of A094617.

Links

• Robert Israel, Table of n, a(n) for n = 0..2092
• Index entries for linear recurrences with constant coefficients, signature (7,-17,17,-6).

Crossrefs

Cf. A094617.

Programs

Maple

seq(3^(n+1) - 2^(n+1) + n + 1, n=0..100); # Robert Israel, Jul 22 2018

Mathematica

Table[3^(n+1)-2^(n+1)+n+1,{n,0,30}] (* or *) LinearRecurrence[{7,-17,17,-6},{2,7,22,69},30] (* Harvey P. Dale, Oct 11 2022 *)

PARI

a(n) = 3^(n+1) - 2^(n+1) + n + 1; \\ Michel Marcus, Jun 05 2016

Formula

a(n) = 2*a(n-1) + 1 - n + 3^n, a(0) = 2.

G.f.: (2-7*x+7*x^2)/(1-7*x+17*x^2-17*x^3+6*x^4). - Robert Israel, Jul 22 2018

From Elmo R. Oliveira, Mar 06 2025: (Start)

E.g.f.: exp(x)*(1 + x + 3*exp(2*x) - 2*exp(x)).

a(n) = 7*a(n-1) - 17*a(n-2) + 17*a(n-3) - 6*a(n-4). (End)

Extensions

New definition from Ralf Stephan, Dec 01 2004