OFFSET
0,2
COMMENTS
Sum of all numbers squared in ordered triples (x,y,z) where 0 <= x <= y <= z <= n.
LINKS
Edward Krogius, Table of n, a(n) for n = 0..999
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
G.f.: 2*x*(7*x+3)/(x-1)^6.
From Amiram Eldar, Sep 11 2022: (Start)
Sum_{n>=1} 1/a(n) = 136/15 - 64*log(2)/5.
Sum_{n>=1} (-1)^(n+1)/a(n) = 16*Pi/5 - 32*log(2)/5 - 82/15. (End)
EXAMPLE
a(1) = 6 because we have the triples (0,0,0), (0,0,1), (0,1,1), (1,1,1).
MATHEMATICA
Table[n*(n + 1)*(n + 2)*(n + 3)*(2*n + 1)/12, {n, 0, 35}] (* Amiram Eldar, Sep 11 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Edward Krogius, Jul 31 2022
STATUS
approved