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A212972 Number of triples (w,x,y) with all terms in {0,...,n} and w >= floor((x+y)/3). 4
1, 8, 24, 53, 100, 168, 261, 384, 540, 733, 968, 1248, 1577, 1960, 2400, 2901, 3468, 4104, 4813, 5600, 6468, 7421, 8464, 9600, 10833, 12168, 13608, 15157, 16820, 18600, 20501, 22528, 24684, 26973, 29400, 31968, 34681, 37544, 40560, 43733 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
For a guide to related sequences, see A212959.
LINKS
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6).
G.f.: (1 + 5x + 3*x^2 + 3*x^3)/((1 + x + x^2)*(1-x)^4).
a(n) = (n+1)^3 - A212971(n).
From Ayoub Saber Rguez, Dec 11 2023: (Start)
a(n) = A011379(n+1) - A212973(n).
a(n) = (2*n^3 + 8*n^2 + 10*n + 4 - (((n+1) mod 3) mod 2))/3. (End)
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w >= Floor[(x + y)/3], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]] (* A212972 *)
CROSSREFS
Sequence in context: A256857 A122655 A280231 * A316541 A152134 A279018
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 03 2012
EXTENSIONS
Name corrected by Ayoub Saber Rguez, Jan 09 2024
STATUS
approved

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Last modified May 22 19:48 EDT 2024. Contains 372758 sequences. (Running on oeis4.)