A164907 a(n) = (3*3^n-(-1)^n)/2.

1, 5, 13, 41, 121, 365, 1093, 3281, 9841, 29525, 88573, 265721, 797161, 2391485, 7174453, 21523361, 64570081, 193710245, 581130733, 1743392201, 5230176601, 15690529805, 47071589413, 141214768241, 423644304721, 1270932914165

Offset: 0

Author

Klaus Brockhaus, Aug 31 2009

Keywords

• nonn
• easy

Comments

Interleaving of A096053 and A083884 without initial term 1.

Partial sums are (essentially) in A080926.

First differences are (essentially) in A105723.

a(n)+a(n+1) = A008776(n+1) = A099856(n+1) = A110593(n+2).

Binomial transform of A056450. Inverse binomial transform of A164908.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (2,3).

Crossrefs

Equals A046717 without initial term 1 and A080925 without initial term 0. Equals A084182 / 2 from second term onward.

Cf. A096053, A083884, A080926, A105723, A008776, A099856, A110593, A056450, A164908.

Programs

Magma

[ (3*3^n-(-1)^n)/2: n in [0..25] ];

Maple

A164907:=n->(3*3^n - (-1)^n)/2; seq(A164907(n), n=0..30); # Wesley Ivan Hurt, Mar 21 2014

Mathematica

Table[(3*3^n - (-1)^n)/2, {n, 0, 30}] (* Wesley Ivan Hurt, Mar 21 2014 *)
LinearRecurrence[{2,3},{1,5},50] (* Harvey P. Dale, Oct 31 2018 *)

Formula

a(n) = 2*a(n-1)+3*a(n-2) for n > 1; a(0) = 1, a(1) = 5.

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

a(n) = 3*a(n-1)+2*(-1)^n. - Carmine Suriano, Mar 21 2014