A086653 a(n) = 2^n + 3*n.

5, 10, 17, 28, 47, 82, 149, 280, 539, 1054, 2081, 4132, 8231, 16426, 32813, 65584, 131123, 262198, 524345, 1048636, 2097215, 4194370, 8388677, 16777288, 33554507, 67108942, 134217809, 268435540, 536870999, 1073741914, 2147483741

Offset: 1

Author

Robert H Rosseau (rhrosseau(AT)yahoo.com), Sep 11 2003

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Crossrefs

Cf. A000079, A008585.

Programs

Maple

seq(2^n + 3*n,n=1..40);

Mathematica

Table[2^n+3n,{n,40}] (* or *) LinearRecurrence[{4,-5,2},{5,10,17},40] (* Harvey P. Dale, Dec 12 2013 *)

Formula

From Colin Barker, Sep 05 2012: (Start)

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).

G.f.: x*(5-10*x+2*x^2)/((1-x)^2*(1-2*x)). (End)

a(n) = A000079(n) + A008585(n). - Michel Marcus, Mar 23 2024

E.g.f.: exp(x)*(exp(x) + 3*x) - 1. - Elmo R. Oliveira, Mar 08 2025

Extensions

More terms from Ray Chandler, Sep 16 2003