A212980 Number of (w,x,y) with all terms in {0,...,n} and w

0, 1, 6, 17, 37, 68, 113, 174, 254, 355, 480, 631, 811, 1022, 1267, 1548, 1868, 2229, 2634, 3085, 3585, 4136, 4741, 5402, 6122, 6903, 7748, 8659, 9639, 10690, 11815, 13016, 14296, 15657, 17102, 18633, 20253, 21964, 23769, 25670, 27670

Offset: 1

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 (3,-2,-2,3,-1).

Crossrefs

Cf. A002620, A212981, A212959.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w < x + y && x < y, s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]   (* A212980 *)

Formula

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

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

From Ayoub Saber Rguez, Oct 08 2021: (Start)

a(n) = A212981(n) - A002620(n+1).

a(n) = (10*n^3 + 15*n^2 + 2*n - 3 + 3*((n+1) mod 2))/24. (End)