A213501 Number of (w,x,y) with all terms in {0,...,n} and w != max(|w-x|, |x-y|).

0, 4, 16, 45, 94, 172, 281, 433, 626, 875, 1177, 1547, 1981, 2497, 3087, 3772, 4543, 5421, 6396, 7492, 8695, 10032, 11488, 13090, 14822, 16714, 18746, 20951, 23308, 25850, 28555, 31459, 34536, 37825, 41299, 44997, 48891, 53023, 57361, 61950, 66757, 71827

Offset: 0

Author

Clark Kimberling, Jun 14 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A212959.

Links

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

Crossrefs

Cf. A212959, A213395.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w != Max[Abs[w - x], Abs[x - y]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]
LinearRecurrence[{1,2,-1,-2,-1,2,1,-1},{0,4,16,45,94,172,281,433},50] (* Harvey P. Dale, Oct 01 2021 *)

Formula

a(n) = a(n-1) + 2*a(n-2) - a(n-3) - 2*a(n-4) - a(n-5) + 2*a(n-6) + a(n-7) - a(n-8).

G.f.: x*(4 + 12*x + 21*x^2 + 21*x^3 + 12*x^4 + 2*x^5)/((1 - x)^4*(1 + x)^2*(1 + x + x^2)).

a(n) = (n+1)^3 - A213395(n).

a(n) = (6*n*(n+1)*(24*n+17) - 9*(2*n+1)*(-1)^n + 32*cos(2*Pi*(n+2)/3) + 25)/144. - Bruno Berselli, Jul 02 2012