A083325 a(n) = 5^n - 4^n + 3^n.

1, 4, 18, 88, 450, 2344, 12258, 63928, 331650, 1710664, 8776098, 44810968, 227894850, 1155188584, 5839863138, 29458185208, 148335970050, 745888724104, 3746365209378, 18799770682648, 94271406797250, 472449572045224, 2366624986030818, 11850654354079288

Offset

0,2

Comments

Binomial transform of A083324.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (12,-47,60).

Formula

a(n) = 5^n - 4^n + 3^n.

G.f.: (1 - 8*x + 17*x^2)/((1 - 3*x)(1 - 4*x)(1 - 5*x)).

E.g.f.: exp(5x) - exp(4x) + exp(3x).

Example

a(2) = 5^2 - 4^2 + 3^2 =  25 - 16 +  9 = 18.
a(3) = 5^3 - 4^3 + 3^3 = 125 - 64 + 27 = 88.

Mathematica

Table[5^n - 4^n + 3^n, {n, 0, 29}] (* Alonso del Arte, Oct 17 2018 *)

Prog

(Magma) [5^n - 4^n + 3^n: n in [0..30]]; // Vincenzo Librandi, Oct 23 2018

Crossrefs

Sequence in context: A130524 A298646 A199309 * A050146 A083879 A363184

Adjacent sequences: A083322 A083323 A083324 * A083326 A083327 A083328

Keyword

easy,nonn

Author

Paul Barry, Apr 27 2003

Status

approved