A199760 a(n) = (9*11^n + 1)/10.
1, 10, 109, 1198, 13177, 144946, 1594405, 17538454, 192922993, 2122152922, 23343682141, 256780503550, 2824585539049, 31070440929538, 341774850224917, 3759523352474086, 41354756877214945, 454902325649364394, 5003925582143008333, 55043181403573091662, 605474995439304008281
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..900
- Index entries for linear recurrences with constant coefficients, signature (12,-11).
Crossrefs
Cf. A199763.
Programs
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Magma
[(9*11^n+1)/10: n in [0..30]];
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Mathematica
(9*11^Range[0, 20] + 1)/10 (* Paolo Xausa, Mar 28 2025 *)
Formula
G.f.: (1-2*x)/((1-x)*(1-11*x)).
a(n) = 12*a(n-1) - 11*a(n-2).
a(n) = 11*a(n-1) - 1.
a(n) = 11^n - Sum_{i=0..n-1} 11^i for n > 0. - Bruno Berselli, Jun 20 2013
From Elmo R. Oliveira, Mar 25 2025: (Start)
E.g.f.: exp(x)*(9*exp(10*x) + 1)/10.
a(n) = A199763(n)/10. (End)