A016308 - OEIS

%I #18 Sep 08 2022 08:44:41

%S 1,19,261,3191,37037,419055,4679557,51894967,573363933,6322119551,

%T 69634013813,766518346503,8434966982989,92804227849807,

%U 1020964052585829,11231309855904599,123548640079779005

%N Expansion of 1/((1-2*x)*(1-6*x)*(1-11*x)).

%H Vincenzo Librandi, <a href="/A016308/b016308.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (19,-100,132).

%F From _Vincenzo Librandi_, Sep 02 2011: (Start)

%F   a(n) = (5*2^n - 81*6^n + 121*11^n)/45.

%F   a(n) = 19*a(n-1) - 100*a(n-2) + 132*a(n-3) for n > 2.

%F   a(n) = 17*a(n-1) - 66*a(n-2) + 2^n. (End)

%F G.f.: 1 + 855*x/(Q(0)-855*x), where Q(k) = x*(10*2^k - 486*6^k + 1331*11^k) + 5*2^k - 81*6^k + 121*11^k - x*(5*2^k - 81*6^k + 121*11^k)*(20*2^k - 2916*6^k + 14641*11^k)/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Jan 02 2014

%o (Magma) [(5*2^n-81*6^n+121*11^n)/45: n in [0..20]]; // _Vincenzo Librandi_, Sep 02 2011

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_