A212889 Number of (w,x,y,z) with all terms in {0,...,n} and even range.

1, 2, 53, 104, 349, 594, 1273, 1952, 3401, 4850, 7501, 10152, 14533, 18914, 25649, 32384, 42193, 52002, 65701, 79400, 97901, 116402, 140713, 165024, 196249, 227474, 266813, 306152, 354901, 403650, 463201, 522752, 594593, 666434

Offset: 0

Author

Clark Kimberling, May 30 2012

Keywords

• nonn
• easy

Comments

a(n)+A212890(n)=(n+1)^4. For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795, A212890.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[#, 2] == 0) &[Max[w, x, y, z] - Min[w, x, y, z]], s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]]   (* A212889 *)

Formula

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

G.f.: f(x)/g(x), where f(x)=-1-47*x^2-47*x^4-x^6 and g(x)=((-1+x)^5)*(1+x)^3.