A212890 Number of (w,x,y,z) with all terms in {0,...,n} and odd range.

0, 14, 28, 152, 276, 702, 1128, 2144, 3160, 5150, 7140, 10584, 14028, 19502, 24976, 33152, 41328, 52974, 64620, 80600, 96580, 117854, 139128, 166752, 194376, 229502, 264628, 308504, 352380, 406350, 460320, 525824, 591328, 669902

Offset

0,2

Comments

a(n) + A212889(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) = 2*a(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)=-7*x-34*x^3-7*x^5 and g(x)=((-1+x)^5)*(1+x)^3.

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[#, 2] == 1) &[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]]   (* A212890 *)
%/2 (* integers *)

Crossrefs

Cf. A211795, A212889.

Sequence in context: A077265 A033847 A067295 * A019552 A325728 A305662

Adjacent sequences: A212887 A212888 A212889 * A212891 A212892 A212893

Keyword

nonn,easy

Author

Clark Kimberling, May 30 2012

Status

approved