OFFSET
2,1
COMMENTS
In general Cos(2Pi*k*r/m)Cos(2Pi*r/m)^n is the number of walks of length n between two nodes at distance k in the cycle graph C_m. Here we have m=10 and k=5. Herbert
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-13,4).
FORMULA
a(n) = 4^n/5*Sum_{r=0..9} (-1)^r*Cos(Pi*r/5)^(2n+1).
a(n) = 7a(n-1)-13a(n-2)+4a(n-3).
G.f.: -2x^2/((-1+4x)(1-3x+x^2)).
a(n) = (8/5)*4^n+2/5*(sqrt(5)-2)*2^n*(3+sqrt(5))^(-n)-2/5*(sqrt(5)+2)*2^n*(3-sqrt(5))^(-n). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 24 2008
MAPLE
f:= gfun:-rectoproc({- a(n) + 7*a(n-1) - 13*a(n-2) + 4*a(n-3), a(2)=2, a(3)=14, a(4)=72}, a(n), remember): map(f, [$2..23]); # Georg Fischer, Jul 16 2020
MATHEMATICA
f[n_]:=FullSimplify[TrigToExp[(4^n/5)Sum[(-1)^k*Cos[Pi*k/5]^(2n+1), {k, 0, 9}]]]; Table[f[n], {n, 1, 35}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Herbert Kociemba, Jul 12 2004
STATUS
approved