%I A141385
%S A141385 3,7,31,157,827,4407,23563,126105,675075,3614143,19349431,103593805,
%T A141385 554625899,2969386479,15897666067,85113810057,455687062275,
%U A141385 2439682811479,13061709929935,69930511268509,374397872321627
%N A141385 A sequence obeying a third-order linear recurrence.
%C A141385 Ruling out finitely many exceptional terms, this sequence differs by 
               a constant from several related enumerations with a slightly more 
               complicated structure (fourth-order linear recurrence):
%C A141385 For n>0, A141221(n)=a(n)-1. For n>2, A141384(n)=a(n)+1.
%H A141385 G. P. Michon, <a href="http://www.numericana.com/answer/graphs.htm#prisms">
               Silent Prisms</a>: A Screaming Game for Short-Sighted People.
%F A141385 Recurrence: a(n+3) = 7*a(n+2)-9*a(n+1)+a(n)
%F A141385 Generating function: (3-14x+9x^2)/(1-7x+9x^2-x^3)
%F A141385 Formula: a(n) = A^n + B^n + C^n
%F A141385 where, putting u = atan(sqrt(5319)/73), we have:
%F A141385 A = 5.3538557854308282... = (7+2*srqt(22)*cos(u/3))/3
%F A141385 B = 1.5235479602692093... = (7-sqrt(22)*cos(u/3)+sqrt(66)*sin(u/3))/3
%F A141385 C = 0.1225962542999624... = (7-sqrt(22)*cos(u/3)-sqrt(66)*sin(u/3))/3
%e A141385 a(0) = 3 = A^0+B^0+C^0
%e A141385 a(1) = 7 = A+B+C
%Y A141385 Cf. A141221, A141384.
%Y A141385 Sequence in context: A000644 A015459 A115083 this_sequence A059296 A123332 
               A051342
%Y A141385 Adjacent sequences: A141382 A141383 A141384 this_sequence A141386 A141387 
               A141388
%K A141385 easy,nice,nonn
%O A141385 0,1
%A A141385 Gerard P. Michon (g.michon(AT)att.net), Jul 02 2008, Jul 23 2008