%I A006499 M2768
%S A006499 1,3,9,12,16,28,49,77,121,198,324,522,841,1363,2209,3572,5776,9348,
%T A006499 15129,24477,39601,64078,103684,167762,271441,439203,710649,1149852,
%U A006499 1860496,3010348,4870849,7881197,12752041,20633238,33385284,54018522
%N A006499 Number of restricted circular combinations.
%D A006499 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006499 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A006499 G. E. Bergum and V. E. Hoggatt, Jr., A combinatorial problem involving 
               recursive sequences and tridiagonal matrices, Fib. Quart., 16 (1978), 
               113-118.
%H A006499 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A006499 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A006499 G.f.: [1+2x+6x^2+2x^3]/[(1+x^2)(1-x-x^2)]. - Ralf Stephan, Apr 23 2004
%F A006499 Lucas(n+2) - I^n - (-I)^n - 1/2*I^(n-1) - 1/2*(-I)^(n-1). - Ralf Stephan, 
               Jun 09 2005
%F A006499 (1/2) {Lucas(n+2) - 3(-1)^[n/2] + (-1)^[(n-1)/2] }. - Ralf Stephan, Jun 
               09 2005
%p A006499 A006499:=-(1+2*z+6*z**2+2*z**3)/(z**2+z-1)/(1+z**2); [Conjectured by 
               S. Plouffe in his 1992 dissertation.]
%t A006499 CoefficientList[ Series[(1 + 2x + 6x^2 + 2x^3)/((1 + x^2)(1 - x - x^2)), 
               {x, 0, 35}], x] (from Robert G. Wilson v Feb 25 2005)
%Y A006499 Equals A000032(n+2) - 2*A056594(n) - A056594(n-1).
%Y A006499 Sequence in context: A136290 A103531 A108860 this_sequence A140979 A096726 
               A155504
%Y A006499 Adjacent sequences: A006496 A006497 A006498 this_sequence A006500 A006501 
               A006502
%K A006499 nonn
%O A006499 0,2
%A A006499 N. J. A. Sloane (njas(AT)research.att.com).
%E A006499 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 25 2005