A212969 Number of (w,x,y) with all terms in {0,...,n} and w != x and x > range(w,x,y).

0, 0, 2, 10, 26, 56, 100, 166, 252, 368, 510, 690, 902, 1160, 1456, 1806, 2200, 2656, 3162, 3738, 4370, 5080, 5852, 6710, 7636, 8656, 9750, 10946, 12222, 13608, 15080, 16670, 18352, 20160, 22066, 24106, 26250, 28536, 30932, 33478, 36140

Offset

0,3

Comments

For a guide to related sequences, see A212959.

Links

Table of n, a(n) for n=0..40.

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

Formula

a(n) = (n-1)*(2*n*(7*n-2) - 3*(-1)^n + 3)/24.

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.: f(x)/g(x), where f(x) = 2*(x^2)*(1 + 3*x + 2*x^2 + x^3) and g(x) = ((1-x)^4)*(1+x)^2.

a(n) = A045991(n) - A212970(n-1). - Ayoub Saber Rguez, Mar 31 2023

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w != x > (Max[w, x, y] - Min[w, x, y]),
  s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]   (* A212969 *)
m/2 (* integers *)

Crossrefs

Cf. A212959, A045991, A212970.

Sequence in context: A069894 A045605 A294871 * A277712 A009307 A131130

Adjacent sequences: A212966 A212967 A212968 * A212970 A212971 A212972

Keyword

nonn,easy

Author

Clark Kimberling, Jun 02 2012

Status

approved