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A213397
Number of (w,x,y) with all terms in {0,...,n} and 2*w >= |x+y-z|.
2
1, 5, 18, 43, 83, 144, 229, 341, 486, 667, 887, 1152, 1465, 1829, 2250, 2731, 3275, 3888, 4573, 5333, 6174, 7099, 8111, 9216, 10417, 11717, 13122, 14635, 16259, 18000, 19861, 21845, 23958, 26203, 28583, 31104, 33769, 36581, 39546, 42667, 45947, 49392, 53005, 56789, 60750
OFFSET
0,2
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.: (1 + 2*x + 6*x^2 + 2*x^3 + x^4)/((1 - x)^4*(1 + x + x^2)).
a(n) = (n+1)^3 - A213396(n).
a(n) = floor(2*n^3/3) + 2*n*(n + 1) + 1. - Bruno Berselli, Dec 22 2017
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[2 w >= Abs[x + y - w], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]] (* A212297 *)
CoefficientList[Series[(1 + 2 x + 6 x^2 + 2 x^3 + x^4)/((1 - x)^4*(1 + x + x^2)), {x, 0, 44}], x] (* Michael De Vlieger, Dec 22 2017 *)
PROG
(PARI) first(n) = Vec((1 + 2*x + 6*x^2 + 2*x^3 + x^4)/((1 - x)^4*(1 + x + x^2)) + O(x^n)) \\ Iain Fox, Dec 22 2017
CROSSREFS
Sequence in context: A272736 A273532 A160969 * A101105 A037140 A321049
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 12 2012
STATUS
approved