A081632 2*3^n-(-1)^n.

1, 7, 17, 55, 161, 487, 1457, 4375, 13121, 39367, 118097, 354295, 1062881, 3188647, 9565937, 28697815, 86093441, 258280327, 774840977, 2324522935, 6973568801, 20920706407, 62762119217, 188286357655, 564859072961, 1694577218887

Offset: 0

Author

Paul Barry, Mar 26 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081631. Inverse binomial transform of A081654.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,3).

Programs

Magma

[2*3^n-(-1)^n: n in [0..40]]; // Vincenzo Librandi, Aug 10 2013

Mathematica

Total/@Partition[Riffle[2*3^Range[0,30],{-1,1}],2] (* or *) LinearRecurrence[{2,3},{1,7},30] (* Harvey P. Dale, May 24 2011 *)
CoefficientList[Series[(1 + 5 x) / ((1 - 3 x) (1 + x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 10 2013 *)

Formula

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

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

a(0)=1, a(1)=7, a(n)=2*a(n-1)+3*a(n-2) [ Harvey P. Dale, May 24 2011]