A117088 a(n) = (11*5^n - 7)/4.
1, 12, 67, 342, 1717, 8592, 42967, 214842, 1074217, 5371092, 26855467, 134277342, 671386717, 3356933592, 16784667967, 83923339842, 419616699217, 2098083496092, 10490417480467, 52452087402342, 262260437011717, 1311302185058592, 6556510925292967
Offset: 0
Examples
If n=1 then 5*(n-1) + 7 = 5*1 + 7 = 12, which is the second term.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-5).
Programs
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Magma
[(11*5^n-7)/4 : n in [0..25]]; // Wesley Ivan Hurt, Nov 12 2014
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Maple
A117088:=n->(11*5^n-7)/4: seq(A117088(n), n=0..25); # Wesley Ivan Hurt, Nov 12 2014
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Mathematica
NestList[5# + 7 &, 1, 50] (* Stefan Steinerberger, Apr 21 2006 *)
Formula
a(n) = 5*a(n-1) + 7 with a(0) = 1.
G.f.: (1+6*x)/((1-x)*(1-5*x)). - Philippe Deléham, Feb 22 2014
a(n) = 6*a(n-1) - 5*a(n-2), a(0) = 1, a(1) = 12. - Philippe Deléham, Feb 22 2014
a(n) = (11*5^n - 7) / 4. - Ralf Stephan, Feb 23 2014
Extensions
Definition corrected and better name by Ralf Stephan, Feb 23 2014