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
Examples
a(2) = 5^2 - 4^2 + 3^2 = 25 - 16 + 9 = 18. a(3) = 5^3 - 4^3 + 3^3 = 125 - 64 + 27 = 88.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (12,-47,60).
Programs
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Magma
[5^n - 4^n + 3^n: n in [0..30]]; // Vincenzo Librandi, Oct 23 2018
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Mathematica
Table[5^n - 4^n + 3^n, {n, 0, 29}] (* Alonso del Arte, Oct 17 2018 *)
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).
Comments