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A212971
Number of triples (w,x,y) with all terms in {0,...,n} and w < floor((x+y)/3).
3
0, 0, 3, 11, 25, 48, 82, 128, 189, 267, 363, 480, 620, 784, 975, 1195, 1445, 1728, 2046, 2400, 2793, 3227, 3703, 4224, 4792, 5408, 6075, 6795, 7569, 8400, 9290, 10240, 11253, 12331, 13475, 14688, 15972, 17328, 18759, 20267, 21853, 23520
OFFSET
0,3
COMMENTS
For a guide to related sequences, see A212959.
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.: (x^2)*(3 + 2*x + x^2)/((1 + x + x^2)*(1-x)^4).
a(n) = (n+1)^3 - A212972(n).
From Ayoub Saber Rguez, Dec 11 2023: (Start)
a(n) = A045991(n+1) - A212974(n).
a(n) = (n^3 + n^2 - n - 1 + (((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]] (* A212971*)
LinearRecurrence[{3, -3, 2, -3, 3, -1}, {0, 0, 3, 11, 25, 48}, 50] (* Harvey P. Dale, Aug 24 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 03 2012
STATUS
approved