cp's OEIS Frontend

A199023 a(n) = (6*11^n - 1)/5.

%I A199023 #26 Mar 07 2025 16:13:37
%S A199023 1,13,145,1597,17569,193261,2125873,23384605,257230657,2829537229,
%T A199023 31124909521,342374004733,3766114052065,41427254572717,
%U A199023 455699800299889,5012697803298781,55139675836286593,606536434199152525,6671900776190677777,73390908538097455549,807299993919072011041
%N A199023 a(n) = (6*11^n - 1)/5.
%C A199023 Sum of n-th row of triangle of powers of 11: 1; 1 11 1; 1 11 121 11 1; 1 11 121 1331 121 11 1; ... - _Philippe Deléham_, Feb 23 2014
%H A199023 Vincenzo Librandi, <a href="/A199023/b199023.txt">Table of n, a(n) for n = 0..900</a>
%H A199023 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-11).
%F A199023 a(n) = 11*a(n-1) + 2.
%F A199023 a(n) = 12*a(n-1) - 11*a(n-2), n > 1.
%F A199023 G.f.: (1 + x)/(1 - 12*x + 11*x^2). - _Vincenzo Librandi_, Jan 04 2013
%F A199023 a(n) = Sum_{k=0..n} A112468(n,k)*12^k. - _Philippe Deléham_, Feb 23 2014
%F A199023 From _Elmo R. Oliveira_, Mar 02 2025: (Start)
%F A199023 E.g.f.: exp(x)*(6*exp(10*x) - 1)/5.
%F A199023 a(n) = A199024(n)/5. (End)
%e A199023 a(0) = 1;
%e A199023 a(1) = 1 + 11 + 1 = 13;
%e A199023 a(2) = 1 + 11 + 121 + 11 + 1 = 145;
%e A199023 a(3) = 1 + 11 + 121 + 1331 + 121 + 11 + 1 = 1597; etc. - _Philippe Deléham_, Feb 23 2014
%t A199023 CoefficientList[Series[(1 + x)/(1 - 12*x + 11*x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 04 2013 *)
%o A199023 (Magma) [(6*11^n-1)/5 : n in [0..20]];
%o A199023 (PARI) a(n)=(6*11^n-1)/5 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A199023 Cf. A112468, A112739, A199024.
%K A199023 nonn,easy
%O A199023 0,2
%A A199023 _Vincenzo Librandi_, Nov 02 2011