A074538 a(n) = 2^n + 5^n + 7^n.
3, 14, 78, 476, 3042, 19964, 133338, 901796, 6155682, 42307244, 292241898, 2026156916, 14085431922, 98109721724, 684326604858, 4778079120836, 33385518525762, 233393453571404, 1632228295438218, 11417968672225556, 79887633730301202, 559022701243584284
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (14,-59,70).
Programs
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Magma
[2^n + 5^n + 7^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011
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Maple
A074538:=n->2^n+5^n+7^n: seq(A074538(n), n=0..30); # Wesley Ivan Hurt, Oct 06 2017
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Mathematica
Table[2^n + 5^n + 7^n, {n, 0, 20}] LinearRecurrence[{14,-59,70},{3,14,78},20] (* Harvey P. Dale, Dec 21 2016 *)
Formula
From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x)+1/(1-5*x)+1/(1-7*x).
E.g.f.: exp(2*x)+exp(5*x)+exp(7*x). (End)
a(n) = 14*a(n-1) - 59*a(n-2) + 70*a(n-3) for n > 2. - Wesley Ivan Hurt, Oct 06 2017