A212254 Number of (w,x,y,z) with all terms in {1,...,n} and w=x+2y+3z-n.

0, 0, 0, 1, 4, 11, 21, 37, 59, 88, 125, 172, 228, 296, 376, 469, 576, 699, 837, 993, 1167, 1360, 1573, 1808, 2064, 2344, 2648, 2977, 3332, 3715, 4125, 4565, 5035, 5536, 6069, 6636, 7236, 7872, 8544, 9253, 10000, 10787, 11613, 12481, 13391

Offset: 0

Author

Clark Kimberling, May 15 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211795.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,0,-1,-1,0,2,-1).

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w == x + 2 y + 3 z - n, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]]  (*  A212254  *)
(* Peter J. C. Moses, Apr 13 2012 *)

Formula

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

G.f.: x^3*(3*x^2+2*x+1)/((x-1)^4*(x+1)*(x^2+x+1)). - Colin Barker, Oct 07 2012