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A212749
Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: w=R, x<R, y<R, z<R, where R = max{w,x,y,z} - min{w,x,y,z}.
2
1, 14, 70, 222, 537, 1116, 2056, 3512, 5605, 8550, 12486, 17694, 24325, 32732, 43072, 55776, 71001, 89262, 110710, 135950, 165121, 198924, 237480, 281592, 331357, 387686, 450646, 521262, 599565, 686700, 782656, 888704, 1004785
OFFSET
0,2
COMMENTS
For a guide to related sequences, see A211795.
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.: ( -1-12*x-40*x^2-60*x^3-37*x^4-12*x^5 ) / ( (1+x)^3*(x-1)^5 ).
MATHEMATICA
t = Compile[{{n, _Integer}},
Module[{s = 0}, (Do[
If[(w == # || x < # || y < # || z < #) &[
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]] (* A212749 *)
(* Peter J. C. Moses, May 24 2012 *)
CROSSREFS
Cf. A211795.
Sequence in context: A236157 A002423 A212751 * A201106 A337641 A213160
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 27 2012
STATUS
approved