OFFSET
0,2
COMMENTS
Limit_{n -> oo} a(n+1)/a(n) does not exist; however, lim_{n -> oo} a(n)^(1/n) = sqrt(5) (conjecture).
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..500
Vaclav Kotesovec, Asymptotic of sequence A084611, Jul 26 2013.
MATHEMATICA
Table[Sum[Abs[Coefficient[Expand[(1+x-x^2)^n], x, k]], {k, 0, 2*n}], {n, 0, 30}] (* Vaclav Kotesovec, Jul 28 2013 *)
PROG
(PARI) {a(n)=sum(k=0, 2*n, abs(polcoeff((1+x-x^2+x*O(x^k))^n, k)))}
for(n=0, 30, print1(a(n), ", "))
(Magma)
A084610:= func< n, k | (&+[Binomial(n, k-j)*Binomial(k-j, j)*(-1)^j: j in [0..k]]) >;
[(&+[Abs(A084610(n, k)): k in [0..2*n]]): n in [0..50]]; // G. C. Greubel, Mar 26 2023
(SageMath)
def A084610(n, k): return sum(binomial(n, j)*binomial(n-j, k-2*j)*(-1)^j for j in range(k//2+1))
[A084611(n) for n in range(50)] # G. C. Greubel, Mar 26 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 01 2003
STATUS
approved