A212978 Number of (w,x,y) with all terms in {0,...,n} and range = 2*n-w-x.

1, 5, 11, 20, 32, 46, 63, 83, 105, 130, 158, 188, 221, 257, 295, 336, 380, 426, 475, 527, 581, 638, 698, 760, 825, 893, 963, 1036, 1112, 1190, 1271, 1355, 1441, 1530, 1622, 1716, 1813, 1913, 2015, 2120, 2228, 2338, 2451, 2567, 2685, 2806, 2930

Offset: 0

Author

Clark Kimberling, Jun 03 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A212959.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Crossrefs

Cf. A212959.

Second bisection of A281333.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Max[w, x, y] - Min[w, x, y] == 2 n - w - x,
  s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]   (* A212978 *)
LinearRecurrence[{2,-1,1,-2,1},{1,5,11,20,32},50] (* Harvey P. Dale, Sep 30 2017 *)

Formula

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).

G.f.: (1 + 3*x + 2*x^2 + 2*x^3)/((1 - x)^3*(1 + x + x^2)). [corrected by Bruno Berselli, Jan 23 2017]