A212970 Number of (w,x,y) with all terms in {0,...,n} and w != x and x < range(w,x,y).

0, 2, 8, 22, 44, 80, 128, 196, 280, 390, 520, 682, 868, 1092, 1344, 1640, 1968, 2346, 2760, 3230, 3740, 4312, 4928, 5612, 6344, 7150, 8008, 8946, 9940, 11020, 12160, 13392, 14688, 16082, 17544, 19110, 20748, 22496, 24320, 26260, 28280

Offset: 0

Author

Clark Kimberling, Jun 02 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A212959.

Twice the partial sums of A210977. - J. M. Bergot, Aug 10 2013

Links

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

Crossrefs

Cf. A088003, A210977, A212959.

Cf. A045991, A212969.

Programs

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]]   (* A212970 *)
m/2 (* essentially A088003 *)

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

a(n) = 2 * A088003(n) for n>0.

From Ayoub Saber Rguez, Mar 31 2023: (Start)

a(n) + A212969(n+1) = A045991(n+1).

a(n) = (10*n^3 + 24*n^2 + 8*n + (6*n)*(n mod 2))/24. (End)

Extensions

Typo in name corrected by Ayoub Saber Rguez, Mar 31 2023