OFFSET
2,1
LINKS
Colin Barker, Table of n, a(n) for n = 2..1000
S. Schlicker, L. Morales, and D. Schultheis, Polygonal chain sequences in the space of compact sets, J. Integer Seq. 12 (2009), no. 1, Article 09.1.7, 23 pp.
Index entries for linear recurrences with constant coefficients, signature (8,-8,1).
FORMULA
G.f.: x^2*(113 - 139*x + 18*x^2)/(1 - 8*x + 8*x^2 - x^3). - M. F. Hasler, Apr 16 2015
a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3) for n>4. - Colin Barker, Aug 05 2020
MAPLE
with(combinat): a := proc(n) local aa, b, c, d, lambda, delta, Q, F, L: F := fibonacci: L := t -> fibonacci(t-1)+fibonacci(t+1): aa := L(2*n)*F(l-2)+F(2*n+2)*F(l-1): b := L(2*n)*F(l-1)+F(2*n+2)*F(l): c := F(2*n+2)*F(l-2)+F(n+2)^2*F(l-1): d := F(2*n+2)*F(l-1)+F(n+2)^2*F(l): Q:=sqrt((d-aa)^2+4*b*c); lambda := (d+aa+Q)/2: delta := (d+aa-Q)/2: : simplify(lambda*((lambda-d)*L(2*n)+b*F(2*n+2))/Q+delta*((lambda-aa)*L(2*n)-b*F(2*n+2))/Q); end proc; # Simplified by M. F. Hasler, Apr 16 2015
MATHEMATICA
LinearRecurrence[{8, -8, 1}, {113, 765, 5234}, 30] (* Paolo Xausa, Jul 22 2024 *)
PROG
(PARI) Vec(x^2*(113 - 139*x + 18*x^2) / ((1 - x)*(1 - 7*x + x^2)) + O(x^20)) \\ Colin Barker, Aug 05 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Steven Schlicker, Dec 15 2008
EXTENSIONS
More terms from M. F. Hasler, Apr 16 2015
STATUS
approved