A233000 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.

16, 5, 25, 20, 81, 125, 400, 845, 2401, 5780, 15625, 39605, 104976, 271445, 714025, 1860500, 4879681, 12752045, 33408400, 87403805, 228886641, 599074580, 1568556025, 4106118245, 10750371856, 28143753125, 73682388025, 192900153620, 505022001201, 1322157322205, 3461460250000, 9062201101805, 23725169980801

Offset

0,1

Links

Table of n, a(n) for n=0..32.

D. Deford, Seating rearrangements on arbitrary graphs, Involve 7(6): 787-805 (2014). See Table 2.

Index entries for linear recurrences with constant coefficients, signature (3,3,-12,0,12,-3,-3,1).

Formula

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

Maple

with(combinat);
L := n->fibonacci(n+1)+fibonacci(n-1);
f:= n-> if (n mod 2) = 0 then (L(n)+2)^2 else L(2*n)+2; fi;
[seq(f(n), n=0..20)];

Crossrefs

Cf. A000032, A000045.

Sequence in context: A070538 A296336 A198064 * A070581 A057995 A097533

Adjacent sequences: A232997 A232998 A232999 * A233001 A233002 A233003

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 17 2013

Status

approved