A082365 A Jacobsthal number sequence.

1, 11, 85, 683, 5461, 43691, 349525, 2796203, 22369621, 178956971, 1431655765, 11453246123, 91625968981, 733007751851, 5864062014805, 46912496118443, 375299968947541, 3002399751580331, 24019198012642645, 192153584101141163

Offset: 0

Author

Paul Barry, Apr 09 2003

Keywords

• easy
• nonn

Comments

A trisection of A024495. - Paul Curtz, Nov 18 2007

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,8).

Crossrefs

Cf. A015565, A082311.

Programs

Magma

[4*8^n/3-(-1)^n/3: n in [0..30]]; // Vincenzo Librandi, Aug 13 2011

Mathematica

f[n_] := (4*8^n - (-1)^n)/3; Array[f, 20, 0] (* Robert G. Wilson v, Aug 13 2011 *)
LinearRecurrence[{7,8},{1,11},20] (* Harvey P. Dale, May 06 2012 *)

PARI

vector(30, n, n--; (4*8^n -(-1)^n)/3) \\ G. C. Greubel, Sep 16 2018

Formula

a(n) = (4*8^n -(-1)^n)/3.

a(n) = J(3*n+2) = A001045(3*n)/3.

a(n) = 4*A015565(n)+A015565(n+1).

From Philippe Deléham, Nov 19 2007: (Start)

a(0)=1, a(1)=11, a(n+1) = 7*a(n) + 8*a(n-1) for n>=1 .

G.f.: (1+4*x)/(1-7*x-8*x^2). (End)