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A213501
Number of (w,x,y) with all terms in {0,...,n} and w != max(|w-x|, |x-y|).
1
0, 4, 16, 45, 94, 172, 281, 433, 626, 875, 1177, 1547, 1981, 2497, 3087, 3772, 4543, 5421, 6396, 7492, 8695, 10032, 11488, 13090, 14822, 16714, 18746, 20951, 23308, 25850, 28555, 31459, 34536, 37825, 41299, 44997, 48891, 53023, 57361, 61950, 66757, 71827
OFFSET
0,2
COMMENTS
For a guide to related sequences, see A212959.
FORMULA
a(n) = a(n-1) + 2*a(n-2) - a(n-3) - 2*a(n-4) - a(n-5) + 2*a(n-6) + a(n-7) - a(n-8).
G.f.: x*(4 + 12*x + 21*x^2 + 21*x^3 + 12*x^4 + 2*x^5))/((1 - x)^4*(1 + x)^2*(1 + x + x^2)).
a(n) = (n+1)^3 - A213395(n).
a(n) = (6*n*(n+1)*(24*n+17) - 9*(2*n+1)*(-1)^n + 32*cos(2*Pi*(n+2)/3) + 25)/144. - Bruno Berselli, Jul 02 2012
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w != Max[Abs[w - x], Abs[x - y]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]
LinearRecurrence[{1, 2, -1, -2, -1, 2, 1, -1}, {0, 4, 16, 45, 94, 172, 281, 433}, 50] (* Harvey P. Dale, Oct 01 2021 *)
CROSSREFS
Sequence in context: A225379 A359073 A134139 * A097125 A213480 A306302
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 14 2012
STATUS
approved