%I #10 Sep 07 2024 12:32:58
%S 16,12,11,17,42,122,365,1095,3284,9848,29535,88589,265742,797190,
%T 2391521,7174499,21523416,64570148,193710323,581130825,1743392306,
%U 5230176722,15690529941,47071589567,141214768412
%N a(0) = 16, a(n+1) = 3a(n) - (6-n)^2.
%D Seen in a newspaper quiz.
%H Harvey P. Dale, <a href="/A028493/b028493.txt">Table of n, a(n) for n = 0..1000</a>
%F From _Chai Wah Wu_, Mar 29 2017: (Start)
%F a(n) = 6*a(n-1) - 12*a(n-2) + 10*a(n-3) - 3*a(n-4) for n > 3.
%F G.f.: (-65*x^3 + 131*x^2 - 84*x + 16)/((x - 1)^3*(3*x - 1)). (End)
%p (3^n + (5-n)*(6-n) + 1)/2;
%t nxt[{n_,a_}]:={n+1,3a-(6-n)^2}; NestList[nxt,{0,16},30][[;;,2]] (* _Harvey P. Dale_, Sep 07 2024 *)
%K nonn,easy
%O 0,1
%A Mark Orr (mjo(AT)cns.ed.ac.uk)
%E Definition edited by _Chai Wah Wu_, Mar 29 2017