A082685 (2*5^n + 2^n)/3.

1, 4, 18, 86, 422, 2094, 10438, 52126, 260502, 1302254, 6510758, 32552766, 162761782, 813804814, 4069015878, 20345063006, 101725282262, 508626345774, 2543131597798, 12715657726846, 63578288109942, 317891439501134

Offset: 0

Author

Paul Barry, Apr 11 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A007583

Row sums of A114195. - Paul Barry, Nov 16 2005

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-10)

Crossrefs

Cf. A001045.

Programs

Mathematica

Table[(2*5^n+2^n)/3,{n,0,30}] (* or *) LinearRecurrence[{7,-10},{1,4},30] (* Harvey P. Dale, Apr 09 2014 *)
CoefficientList[Series[(1 - 3 x)/((1 - 5 x) (1 - 2 x)), {x, 0, 50}], x] (* Vincenzo Librandi, Apr 10 2014 *)

PARI

a(n)=(2*5^n+2^n)/3 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (1-3x)/((1-5x)(1-2x))

a(n)=sum{k=0..n, sum{j=0..n, C(n, j)C(j+k, 2k)2^(j-k)}}. - Paul Barry, Nov 16 2005

a(0)=1, a(1)=4, a(n)=7*a(n-1)-10*a(n-2). - Harvey P. Dale, Apr 09 2014