A137208 a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) for n > 2; a(0)=2, a(1)=3, a(2)=6.

2, 3, 6, 10, 22, 38, 86, 150, 342, 598, 1366, 2390, 5462, 9558, 21846, 38230, 87382, 152918, 349526, 611670, 1398102, 2446678, 5592406, 9786710, 22369622, 39146838, 89478486, 156587350, 357913942, 626349398, 1431655766, 2505397590, 5726623062, 10021590358

Offset: 0

Author

Paul Curtz, Mar 05 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 4, -4).

Crossrefs

Cf. A097164.

Programs

Magma

[(2/3)+(5/4)*2^n+(1/12)*(-2)^n: n in [0..40]]; // Vincenzo Librandi, Aug 09 2011

Maple

a:=proc(n) option remember; if n=0 then 2 elif n=1 then 3 elif n=2 then 6 else a(n-1)+4*a(n-2)-4*a(n-3); fi; end: seq(a(n), n=0..50); # Wesley Ivan Hurt, Jan 21 2017

Mathematica

LinearRecurrence[{1,4,-4},{2,3,6},40] (* Harvey P. Dale, Sep 04 2018 *)

PARI

Vec((2 + x - 5*x^2) / ((1 - x)*(1 - 2*x)*(1 + 2*x)) + O(x^40)) \\ Colin Barker, Jan 22 2017

Formula

G.f.: (2 + x - 5*x^2) / ((1 - x)*(1 - 2*x)*(1 + 2*x)). - Colin Barker, Jan 22 2017

Extensions

Extended by Vincenzo Librandi, Aug 09 2011