A199023 a(n) = (6*11^n - 1)/5.
1, 13, 145, 1597, 17569, 193261, 2125873, 23384605, 257230657, 2829537229, 31124909521, 342374004733, 3766114052065, 41427254572717, 455699800299889, 5012697803298781, 55139675836286593, 606536434199152525, 6671900776190677777, 73390908538097455549, 807299993919072011041
Offset: 0
Examples
a(0) = 1; a(1) = 1 + 11 + 1 = 13; a(2) = 1 + 11 + 121 + 11 + 1 = 145; a(3) = 1 + 11 + 121 + 1331 + 121 + 11 + 1 = 1597; etc. - _Philippe Deléham_, Feb 23 2014
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..900
- Index entries for linear recurrences with constant coefficients, signature (12,-11).
Programs
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Magma
[(6*11^n-1)/5 : n in [0..20]];
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Mathematica
CoefficientList[Series[(1 + x)/(1 - 12*x + 11*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *) -
PARI
a(n)=(6*11^n-1)/5 \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = 11*a(n-1) + 2.
a(n) = 12*a(n-1) - 11*a(n-2), n > 1.
G.f.: (1 + x)/(1 - 12*x + 11*x^2). - Vincenzo Librandi, Jan 04 2013
a(n) = Sum_{k=0..n} A112468(n,k)*12^k. - Philippe Deléham, Feb 23 2014
From Elmo R. Oliveira, Mar 02 2025: (Start)
E.g.f.: exp(x)*(6*exp(10*x) - 1)/5.
a(n) = A199024(n)/5. (End)
Comments