A211438 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w+2x+2y=0.

1, 3, 13, 19, 39, 49, 79, 93, 133, 151, 201, 223, 283, 309, 379, 409, 489, 523, 613, 651, 751, 793, 903, 949, 1069, 1119, 1249, 1303, 1443, 1501, 1651, 1713, 1873, 1939, 2109, 2179, 2359, 2433, 2623, 2701, 2901, 2983, 3193, 3279, 3499, 3589

Offset: 0

Author

Clark Kimberling, Apr 11 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211422.

Crossrefs

Cf. A211422.

Programs

Mathematica

t[n_] := t[n] = Flatten[Table[w + 2 x + 2 y, {w, -n, n}, {x, -n, n}, {y, -n, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 70}]  (* A211438 *)
(t - 1)/2                    (* A118277  *)

Formula

Conjecture: a(n) = (5+3*(-1)^n+2*(7+3*(-1)^n)*n+14*n^2)/8. G.f.: (1+2*x+8*x^2+2*x^3+x^4)/((1-x)^3*(1+x)^2). [Colin Barker, Apr 18 2012]