A212975 Number of (w,x,y) with all terms in {0,...,n} and even range.

1, 2, 15, 28, 65, 102, 175, 248, 369, 490, 671, 852, 1105, 1358, 1695, 2032, 2465, 2898, 3439, 3980, 4641, 5302, 6095, 6888, 7825, 8762, 9855, 10948, 12209, 13470, 14911, 16352, 17985, 19618, 21455, 23292, 25345, 27398, 29679, 31960

Offset: 0

Author

Clark Kimberling, Jun 03 2012

Keywords

• nonn
• easy

Comments

a(n)+A212976(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, A212976.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Mod[Max[w, x, y] - Min[w, x, y], 2] == 0,
   s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]   (* A212975 *)

Formula

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

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) = 1 + 10*x^2 + x^4 and g(x) = ((1-x)^4)*(1+x)^2.