A211516 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2=x+y.

0, 0, 1, 3, 3, 5, 7, 9, 12, 14, 16, 18, 20, 24, 28, 32, 34, 36, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 96, 102, 108, 114, 118, 122, 126, 130, 134, 140, 146, 152, 158, 164, 170, 176, 182, 186, 191, 197, 203, 209, 215, 221, 227, 233, 239, 245

Offset

0,4

Comments

For a guide to related sequences, see A211422.

Links

Table of n, a(n) for n=0..59.

Formula

Conjecture: a(n) = -(2*n + 5/3)*w(n) + w(n)^2 + (2/3)*w(n)^3 + (2*n + 5/6)*w(2*n) - (1/2)*w(2*n)^2 - (1/3)*w(2*n)^3, where w = A000196. - Velin Yanev, Nov 16 2021

Mathematica

t[n_] := t[n] = Flatten[Table[w^2 - x - y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 70}]  (* A211516 *)

Crossrefs

Cf. A211422.

Sequence in context: A333147 A323434 A323431 * A323430 A291941 A355225

Adjacent sequences: A211513 A211514 A211515 * A211517 A211518 A211519

Keyword

nonn

Author

Clark Kimberling, Apr 14 2012

Status

approved