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A356251
a(n) = n*(n+1)*(n+2)*(n+3)*(2*n+1)/12.
1
0, 6, 50, 210, 630, 1540, 3276, 6300, 11220, 18810, 30030, 46046, 68250, 98280, 138040, 189720, 255816, 339150, 442890, 570570, 726110, 913836, 1138500, 1405300, 1719900, 2088450, 2517606, 3014550, 3587010, 4243280, 4992240, 5843376, 6806800, 7893270, 9114210
OFFSET
0,2
COMMENTS
Sum of all numbers squared in ordered triples (x,y,z) where 0 <= x <= y <= z <= n.
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
Cf. A033487.
Sequence in context: A062801 A035290 A138422 * A001303 A220887 A213807
KEYWORD
nonn,easy
AUTHOR
Edward Krogius, Jul 31 2022
STATUS
approved