A105280 a(0)=0; a(n) = 11*a(n-1) + 11.
0, 11, 132, 1463, 16104, 177155, 1948716, 21435887, 235794768, 2593742459, 28531167060, 313842837671, 3452271214392, 37974983358323, 417724816941564, 4594972986357215, 50544702849929376, 555991731349223147, 6115909044841454628, 67274999493256000919, 740024994425816010120
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..960
- Index entries for linear recurrences with constant coefficients, signature (12,-11).
Programs
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Maple
a:=n-> add(11^j,j=1..n): seq(a(n),n=0..12); # Zerinvary Lajos, Oct 03 2007
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Mathematica
NestList[11#+11&,0,20] (* or *) LinearRecurrence[{12,-11},{0,11},20] (* Harvey P. Dale, Dec 02 2023 *)
Formula
a(n) = 11^n + a(n-1) (with a(0)=0). - Vincenzo Librandi, Nov 13 2010
From Elmo R. Oliveira, May 24 2025: (Start)
G.f.: 11*x/((x-1)*(11*x-1)).
E.g.f.: 11*exp(x)*(exp(10*x) - 1)/10.
a(n) = 11*(11^n - 1)/10.
a(n) = 12*a(n-1) - 11*a(n-2).
a(n) = A016123(n) - 1. (End)
Extensions
Corrected by T. D. Noe, Nov 07 2006