%I #22 Mar 28 2024 16:11:56

%S 1,3,8,24,75,233,714,2166,6533,19647,59004,177092,531375,1594245,

%T 4782878,14348802,43046601,129140027,387420336,1162261296,3486784211,

%U 10460352993,31381059378,94143178574,282429536205,847288609143,2541865828004,7625597484636,22876792454583,68630377364477,205891132094214,617673396283482,1853020188851345,5559060566554995

%N a(n) = 3^n - n*(n-1)/2.

%C For n>0, r(n)=a(n)/a(n-1) is approximately equal to 3. Average of the sum of r(n) is 3. Except for r(3) = 2.666666666666667, all other r(n)'s are just above zero and r(n) tends to 3 as n tends to infinity.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,10,-3).

%F G.f.: (1-3*x+2*x^2+2*x^3)/((1-x)^3*(1-3*x)). - _Colin Barker_, May 07 2012

%e For n=6, a(n)=714, a(n-1)=233, r(n)=3.0643776824034334763948497854077.

%e For n=21, a(n)=10460352993, a(n-1)=3486784211, r(n) = 3.0000001032469972946083183924341.

%K nonn,easy

%O 0,2

%A _Aditya Subramanian_, Apr 29 2012

%E Edited by _N. J. A. Sloane_, May 01 2012