%I A092936
%S A092936 1,9,100,1089,11881,129600,1413721,15421329,168220900,1835008569,
%T A092936 20016873361,218350598400,2381839709041,25981886201049,283418908502500,
%U A092936 3091626107326449,33724468272088441,367877524885646400
%N A092936 Area of n-th triple of hexagons around a triangle.
%C A092936 This is the unsigned member r=-9 of the family of Chebyshev sequences 
               S_r(n) defined in A092184: ((-1)^(n+1))*a(n) = S_{-9}(n), n>=0.
%F A092936 a(n)=10*(a(n-1)+a(n-2))-a(n-3), a(1)=1, a(2)=9, a(3)=100. G.f.: (1-x)*x/
               (1-10*x-10*x^2+x^3). a(n)=((3-Sqrt(13))^n-(3+Sqrt(13))^n)^2/(13*4^n)
%F A092936 a(n)= 2*(T(n, 11/2)-(-1)^n)/13 with twice the Chebyshev's polynomials 
               of the first kind evaluated at x=11/2: 2*T(n, 11/2)=A057076(n)=((11+3*sqrt(13))^n 
               + (11-3*sqrt(13))^n)/2^n. W. Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Oct 18 2004
%e A092936 a(5)=10*(1089+100)-9=11881. From A006190, a(5)=(3*33+10)^2=11881
%p A092936 seq(fibonacci(n,3)^2,n=1..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 05 2008
%t A092936 CoefficientList[Series[(1-x)*x/(1-10*x-10*x^2+x^3), {x, 0, 20}], x] (CoefficientList[Series[x/
               (1-3*x-x^2), {x, 0, 20}], x])^2 Table[Round[((3+Sqrt[13])^n)^2/(13*4^n)], 
               {n, 1, 20}]
%Y A092936 Equals (A006190)^2
%Y A092936 Cf. A005386, A006190.
%Y A092936 Sequence in context: A017018 A027769 A065736 this_sequence A056002 A060150 
               A103461
%Y A092936 Adjacent sequences: A092933 A092934 A092935 this_sequence A092937 A092938 
               A092939
%K A092936 easy,nonn
%O A092936 1,2
%A A092936 Peter J. C. Moses. (mows(AT)mopar.freeserve.co.uk), Apr 18 2004