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

0,2

Comments

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

Links

Table of n, a(n) for n=0..33.

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.

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 *)

Crossrefs

Cf. A211795, A212890.

Sequence in context: A167771 A062853 A059703 * A041337 A139844 A249657

Adjacent sequences: A212886 A212887 A212888 * A212890 A212891 A212892

Keyword

nonn,easy

Author

Clark Kimberling, May 30 2012

Status

approved