OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 1/((1-4*x*g^3) * (1+x*g^5)) where g = 1+x*g^4 is the g.f. of A002293.
a(n) = Sum_{k=0..n} binomial(2*n+2*k-2,k).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(4*n-k-1,n-2*k).
MATHEMATICA
Table[Sum[(-1)^k*Binomial[4*n+k, n-k], {k, 0, n}], {n, 0, 22}] (* Vincenzo Librandi, Nov 11 2025 *)
PROG
(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(4*n+k, n-k));
(Magma) [&+[(-1)^k*Binomial(4*n+k, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 11 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 10 2025
STATUS
approved
