OFFSET
0,4
FORMULA
a(n) = sum(binomial(2*k,k)*sum(binomial(n+k-i,2*k)*binomial(n-k-i,2*i)*(-1)^(n-k-i),i=0..floor((n-k)/3)),k=0..n).
G.f.: sqrt((1-2*x+x^2+x^3+sqrt(1-4*x+6*x^2-6*x^3-11*x^4-2*x^5+x^6))/(2*(1-4*x+6*x^2-6*x^3-11*x^4-2*x^5+x^6))).
MATHEMATICA
Table[Sum[Binomial[n-k, 2k]^2, {k, 0, Floor[n/3]}], {n, 0, 100}]
a[n_] := HypergeometricPFQ[ ({1, 1, 2, 2, 0, 0}-n)/3, {1/2, 1/2, 1, -n, -n}, 729/16]; Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Feb 22 2013 *)
PROG
(Maxima) makelist(sum(binomial(n-k, 2*k)^2, k, 0, floor(n/3)), n, 0, 26);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, May 31 2011
STATUS
approved