%I #12 Mar 15 2024 11:46:17
%S 0,4,14,40,110,304,854,2440,7070,20704,61094,181240,539630,1610704,
%T 4815734,14414440,43177790,129402304,387944774,1163310040,3488881550,
%U 10464547504,31389448214,94159956040,282463090910,847355718304
%N a(n) = 3^n+2*2^n-3.
%D G. S. Carr, Formulas and Theorems in Pure Mathematics, New York, Chelsea, 1970. see pp. 83-84.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F G.f.: x * (4 - 10*x) / ((1 - x) * (1 - 2*x) * (1 - 3*x)).
%F a(0)=0, a(1)=4, a(2)=14, a(n)=6*a(n-1)-11*a(n-2)+6*a(n-3). - _Harvey P. Dale_, Sep 06 2012
%e 4*x + 14*x^2 + 40*x^3 + 110*x^4 + 304*x^5 + 854*x^6 + 2440*x^7 + 7070*x^8 + ...
%t Table[3^n+2*2^n-3,{n,0,30}] (* or *) LinearRecurrence[{6,-11,6},{0,4,14},30] (* _Harvey P. Dale_, Sep 06 2012 *)
%o (PARI) {a(n) = 3^n + 2 * 2^n - 3}
%K nonn,easy
%O 0,2
%A _Michael Somos_, Jul 01 2002