A213390 Number of (w,x,y) with all terms in {0,...,n} and max(w,x,y) >= 2*min(w,x,y).

1, 7, 25, 55, 109, 181, 289, 421, 601, 811, 1081, 1387, 1765, 2185, 2689, 3241, 3889, 4591, 5401, 6271, 7261, 8317, 9505, 10765, 12169, 13651, 15289, 17011, 18901, 20881, 23041, 25297, 27745, 30295, 33049, 35911, 38989, 42181, 45601

Offset: 0

Author

Clark Kimberling, Jun 11 2012

Keywords

• nonn
• easy

Comments

a(n)+A213389(n) = (n+1)^3.

For a guide to related sequences, see A212959.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Crossrefs

Cf. A212959.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Max[w, x, y] >= 2*Min[w, x, y], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 50]]   (* A213390 *)

Formula

a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).

G.f.: (1 + 5*x + 10*x^2 + 2*x^3 + x^4 - x^5)/((1 - x)^4*(1 + x)^2).

a(n) = (6*n^3+24*n^2+21*n+8+3*n*(-1)^n)/8. - Luce ETIENNE, Jul 17 2016