A211439 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w+3x+3y=0.

1, 3, 5, 19, 25, 31, 59, 69, 79, 121, 135, 149, 205, 223, 241, 311, 333, 355, 439, 465, 491, 589, 619, 649, 761, 795, 829, 955, 993, 1031, 1171, 1213, 1255, 1409, 1455, 1501, 1669, 1719, 1769, 1951, 2005, 2059, 2255, 2313, 2371, 2581, 2643, 2705

Offset: 0

Author

Clark Kimberling, Apr 11 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A211422.

Crossrefs

Cf. A211422.

Programs

Mathematica

t[n_] := t[n] = Flatten[Table[w + 3 x + 3 y, {w, -n, n}, {x, -n, n}, {y, -n, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 70}]  (* A211439 *)
(t - 1)/2                    (* integers *)

Formula

Conjectures from Colin Barker, May 15 2017: (Start)

G.f.: (1 + 2*x + 2*x^2 + 12*x^3 + 2*x^4 + 2*x^5 + x^6) / ((1 - x)^3*(1 + x + x^2)^2).

a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7) for n>6.

(End)