OFFSET
2,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 2..1000
FORMULA
From Vaclav Kotesovec, Oct 14 2017: (Start)
a(n) = 6*a(n-1) - 10*a(n-2) + 4*a(n-3).
a(n) ~ 2^(n/2 - 2) * (1+sqrt(2))^(n+1).
a(n) = 2^(n/2 - 2) * ((sqrt(2)+1)^(n+1) - (sqrt(2)-1)^(n+1)) - 2^n.
(End)
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1,
add(b(n-j, k)*binomial(j+k-1, k-1), j=1..n))
end:
a:= n-> (k->add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k))(2):
seq(a(n), n=2..30);
MATHEMATICA
Table[Simplify[2^(n/2 - 2)*((Sqrt[2]+1)^(n+1) - (Sqrt[2]-1)^(n+1)) - 2^n], {n, 2, 20}] (* Vaclav Kotesovec, Oct 14 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 12 2017
STATUS
approved