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A213481
Number of triples (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| <= w+x+y.
3
1, 7, 25, 59, 117, 202, 323, 482, 689, 945, 1261, 1637, 2085, 2604, 3207, 3892, 4673, 5547, 6529, 7615, 8821, 10142, 11595, 13174, 14897, 16757, 18773, 20937, 23269, 25760, 28431, 31272, 34305, 37519, 40937, 44547, 48373, 52402, 56659
OFFSET
0,2
COMMENTS
For a guide to related sequences, see A212959.
FORMULA
a(n) + A006918(n) = (n+1)^3.
a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
G.f.: (1 + 5*x + 10*x^2 + 6*x^3 + x^4)/((1 - x)^4*(1 + x)^2).
From Ayoub Saber Rguez, Dec 29 2021: (Start)
a(n) = A213482(n) + A213479(n).
a(n) = (23*n^3 + 66*n^2 + 64*n + 24 - (3*n+6)*(n mod 2))/24. (End)
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w + x + y >= Abs[w - x] + Abs[x - y], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
Map[t[#] &, Range[0, 60]] (* A213481 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 13 2012
STATUS
approved