A233000 - OEIS

%I #21 Feb 10 2024 03:44:00

%S 16,5,25,20,81,125,400,845,2401,5780,15625,39605,104976,271445,714025,

%T 1860500,4879681,12752045,33408400,87403805,228886641,599074580,

%U 1568556025,4106118245,10750371856,28143753125,73682388025,192900153620,505022001201,1322157322205,3461460250000,9062201101805,23725169980801

%N Let L(n) = Fibonacci(n-1)+Fibonacci(n+1) (cf. A000045, A000032); if n is even then a(n) = (L(n)+2)^2 otherwise a(n) = L(2*n)+2.

%H D. Deford, <a href="http://dx.doi.org/10.2140/involve.2014.7.787">Seating rearrangements on arbitrary graphs</a>, Involve 7(6): 787-805 (2014). See Table 2.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,-12,0,12,-3,-3,1).

%F G.f.: -(5*x^7 +10*x^6 -70*x^5 +6*x^4 +122*x^3 -38*x^2 -43*x +16) / ((x -1)*(x +1)*(x^2 -3*x +1)*(x^2 -x -1)*(x^2 +x -1)). - _Colin Barker_, Sep 12 2014

%p with(combinat);

%p L := n->fibonacci(n+1)+fibonacci(n-1);

%p f:= n-> if (n mod 2) = 0 then (L(n)+2)^2 else L(2*n)+2; fi;

%p [seq(f(n),n=0..20)];

%Y Cf. A000032, A000045.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, Dec 17 2013