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A213484
Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| + |y-w| >= w+x+y.
3
1, 4, 7, 10, 16, 25, 34, 43, 55, 70, 85, 100, 118, 139, 160, 181, 205, 232, 259, 286, 316, 349, 382, 415, 451, 490, 529, 568, 610, 655, 700, 745, 793, 844, 895, 946, 1000, 1057, 1114, 1171, 1231, 1294, 1357, 1420, 1486, 1555, 1624, 1693, 1765
OFFSET
0,2
COMMENTS
a(n) + A213485(n) = (n+1)^3.
For a guide to related sequences, see A212959.
FORMULA
a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5).
G.f.: (1 + x - x^2 + x^3 + x^4)/((1 - x)^3 (1 + x^2)).
From Ayoub Saber Rguez, Dec 31 2021: (Start)
a(n) + A213485(n) = (n+1)^3.
a(n) = 3*A054925(n+1) + 1.
a(n) = 3*(A192447(n+1)/2) + 1.
a(n) = (3*n^2 + 3*n + 4 + 3*((n+1) mod 4 - (n+1) mod 2))/4. (End)
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w + x + y == Abs[w - x] + Abs[x - y] + Abs[y - w],
s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
Map[t[#] &, Range[0, 60]] (* A213484 *)
CROSSREFS
Cf. A212959.
Sequence in context: A310713 A180080 A153003 * A362255 A128429 A191154
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 13 2012
STATUS
approved