A198695 a(n) = 11*4^n - 1.
10, 43, 175, 703, 2815, 11263, 45055, 180223, 720895, 2883583, 11534335, 46137343, 184549375, 738197503, 2952790015, 11811160063, 47244640255, 188978561023, 755914244095, 3023656976383, 12094627905535, 48378511622143, 193514046488575, 774056185954303, 3096224743817215
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-4).
Programs
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Magma
[11*4^n-1: n in [0..30]];
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Mathematica
11*4^Range[0,30]-1 (* or *) NestList[4#+3&,10,30] (* or *) LinearRecurrence[ {5,-4},{10,43},30] (* Harvey P. Dale, Aug 07 2021 *)
Formula
a(n) = 4*a(n-1) + 3.
a(n) = 5*a(n-1) - 4*a(n-2), n > 1.
G.f.: (10-7*x)/((4*x-1)*(x-1)). - R. J. Mathar, Oct 30 2011
From Elmo R. Oliveira, May 07 2025: (Start)
E.g.f.: exp(x)*(11*exp(3*x) - 1).
a(n) = A199211(n) - 2. (End)