OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,2,-1,1).
FORMULA
G.f.: (1-x^2)/(1-x-2*x^2-2*x^3+x^4-x^5).
a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..k} C(2*n-4*k,j)*C(k,j)*2^j.
a(n) = Sum_{k=0..floor(n/2)} Hypergeometric2F1([-k, 2*(k-n)], [1], 2). - G. C. Greubel, Nov 19 2021
MATHEMATICA
LinearRecurrence[{1, 2, 2, -1, 1}, {1, 1, 2, 6, 11}, 45] (* G. C. Greubel, Nov 19 2021 *)
PROG
(Magma)
A184883:= func< n, k | (&+[Binomial(k, j)*Binomial(2*(n-k), j)*2^j: j in [0..k]]) >;
[A184884(n): n in [0..40]]; // G. C. Greubel, Nov 19 2021
(Sage)
def A184883(n, k): return simplify( hypergeometric([-k, 2*(k-n)], [1], 2) )
[A184884(n) for n in (0..40)] # G. C. Greubel, Nov 19 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Jan 24 2011
STATUS
approved