A211481 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w+2x+3y=n.

1, 3, 8, 16, 26, 38, 54, 71, 91, 114, 139, 166, 197, 229, 264, 302, 342, 384, 430, 477, 527, 580, 635, 692, 753, 815, 880, 948, 1018, 1090, 1166, 1243, 1323, 1406, 1491, 1578, 1669, 1761, 1856, 1954, 2054, 2156, 2262, 2369, 2479, 2592, 2707

Offset: 0

Author

Clark Kimberling, Apr 12 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A211422.

Crossrefs

Cf. A211422.

Programs

Mathematica

t[n_] := t[n] = Flatten[Table[w + 2 x + 3 y - n, {w, -n, n}, {x, -n, n}, {y, -n, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 70}]  (* A211481 *)

Formula

Conjecture: a(n) = a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6) for n>5. - Colin Barker, Nov 08 2014

Empirical g.f.: -(3*x^4+5*x^3+4*x^2+2*x+1) / ((x-1)^3*(x+1)*(x^2+x+1)). - Colin Barker, Nov 08 2014