%I #20 Sep 08 2022 08:46:00
%S 1,13,145,1597,17569,193261,2125873,23384605,257230657,2829537229,
%T 31124909521,342374004733,3766114052065,41427254572717,
%U 455699800299889,5012697803298781,55139675836286593,606536434199152525
%N (6*11^n - 1) / 5.
%C 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 Vincenzo Librandi, <a href="/A199023/b199023.txt">Table of n, a(n) for n = 0..900</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-11).
%F a(n) = 11*a(n-1)+2.
%F a(n) = 12*a(n-1)-11*a(n-2), n>1.
%F G.f.: (1 + x)/(1 - 12*x + 11*x^2). - _Vincenzo Librandi_, Jan 04 2013
%F a(n) = Sum_{k=0..n} A112468(n,k)*12^k. - _Philippe Deléham_, Feb 23 2014
%e a(0) = 1;
%e a(1) = 1 + 11 + 1 = 13;
%e a(2) = 1 + 11 + 121 + 11 + 1 = 145;
%e a(3) = 1 + 11 + 121 + 1331 + 121 + 11 + 1 = 1597; etc. - _Philippe Deléham_, Feb 23 2014
%t CoefficientList[Series[(1 + x)/(1 - 12*x + 11*x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 04 2013 *)
%o (Magma) [(6*11^n-1)/5 : n in [0..20]]
%o (PARI) a(n)=(6*11^n-1)/5 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A112468, A112739.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Nov 02 2011