A199317 a(n) = 2*6^n + 1.

3, 13, 73, 433, 2593, 15553, 93313, 559873, 3359233, 20155393, 120932353, 725594113, 4353564673, 26121388033, 156728328193, 940369969153, 5642219814913, 33853318889473, 203119913336833, 1218719480020993, 7312316880125953, 43873901280755713

Offset: 0

Author

Vincenzo Librandi, Nov 05 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-6).

Crossrefs

Cf. A000400, A062394, A167747.

Programs

Magma

[2*6^n+1: n in [0..30]];

Mathematica

2 6^Range[0,30]+1 (* or *) LinearRecurrence[{7,-6},{3,13},30] (* Harvey P. Dale, Jul 02 2023 *)

Formula

a(n) = 6*a(n-1)-5.

a(n) = 7*a(n-1)-6*a(n-2).

G.f.: (3-8*x)/((1-x)*(1-6*x)).

a(n) = 1 + A167747(n+1) = 1 + 2*A000400(n) = A000400(n) + A062394(n). - Alois P. Heinz, Jul 02 2023