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A212742
Number of (w,x,y,z) with all terms in {0,...,n} and max{w,x,y,z}<=2*min{w,x,y,z}.
3
1, 2, 17, 32, 97, 162, 337, 512, 881, 1250, 1921, 2592, 3697, 4802, 6497, 8192, 10657, 13122, 16561, 20000, 24641, 29282, 35377, 41472, 49297, 57122, 66977, 76832, 89041, 101250, 116161, 131072, 149057, 167042, 188497, 209952, 235297
OFFSET
0,2
COMMENTS
Also, the number of (w,x,y,z) with all terms in {0,...,n} and the differences w-x, x-y, y-z all even.
a(n)+A212743(n) = n^4.
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+x^2)*(x^4+10*x^2+1) / ( (1+x)^3*(x-1)^5 ).
a(n) = A212740(n+1) for n>=0.
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Max[w, x, y, z] <= 2 Min[w, x, y, z], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]] (* A212742 *)
LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {1, 2, 17, 32, 97, 162, 337, 512}, 40] (* Harvey P. Dale, May 14 2013 *)
CROSSREFS
Cf. A211795.
Sequence in context: A003336 A344187 A212740 * A178145 A055261 A307690
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 26 2012
STATUS
approved