A047082 a(n) = Sum_{i=0..floor(n/2)} A047080(n,i).

1, 1, 2, 3, 7, 10, 23, 34, 76, 115, 253, 389, 845, 1316, 2829, 4452, 9488, 15061, 31863, 50951, 107112, 172366, 360360, 583110, 1213150, 1972647, 4086217, 6673417, 13769519, 22576008, 46416937, 76374088, 156520328, 258371689, 527937429, 874065163, 1781131638

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Mathematica

A[n_, k_]:= Sum[(-1)^j*(n+k-3*j)!/(j!*(n-2*j)!*(k-2*j)!), {j, 0, Floor[(n+k)/3]}] - Sum[(-1)^j*(n+k-3*j-2)!/(j!*(n-2*j-1)!*(k-2*j-1)!), {j, 0, Floor[(n+k-2)/3]}];
A047082[n_]:= A047082[n]= Sum[A[n-k, k], {k, 0, Floor[n/2]}];
Table[A047082[n], {n, 0, 50}] (* G. C. Greubel, Oct 31 2022 *)

Prog

(Magma)
F:=Factorial;
p:= func< n, k | (&+[ (-1)^j*F(n+k-3*j)/(F(j)*F(n-2*j)*F(k-2*j)): j in [0..Min(Floor(n/2), Floor(k/2))]]) >;
q:= func< n, k | n eq 0 or k eq 0 select 0 else (&+[ (-1)^j*F(n+k-3*j-2)/(F(j)*F(n-2*j-1)*F(k-2*j-1)) : j in [0..Min(Floor((n-1)/2), Floor((k-1)/2))]]) >;
A:= func< n, k | p(n, k) - q(n, k) >;
[(&+[A(n-j, j): j in [0..Floor(n/2)]]): n in [0..50]]; // G. C. Greubel, Oct 31 2022
(SageMath)
f=factorial
def p(n, k): return sum( (-1)^j*f(n+k-3*j)/(f(j)*f(n-2*j)*f(k-2*j)) for j in range(1+min((n//2), (k//2))) )
def q(n, k): return sum( (-1)^j*f(n+k-3*j-2)/(f(j)*f(n-2*j-1)*f(k-2*j-1)) for j in range(1+min(((n-1)//2), ((k-1)//2))) )
def A(n, k): return p(n, k) - q(n, k)
[sum(A(n-j, j) for j in range(1+(n//2))) for n in range(51)] # G. C. Greubel, Oct 31 2022

Crossrefs

Cf. A047080, A047081, A047083, A047084, A047085, A047086, A047087, A047088.

Sequence in context: A365967 A079380 A263402 * A062113 A346799 A130968

Adjacent sequences: A047079 A047080 A047081 * A047083 A047084 A047085

Keyword

nonn

Author

Clark Kimberling

Extensions

Data corrected by Sean A. Irvine, May 11 2021

Status

approved