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 A213501 Number of (w,x,y) with all terms in {0,...,n} and w != max(|w-x|,|x-y|) 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n)+A213395(n) = (n+1)^3. For a guide to related sequences, see A212959. LINKS Table of n, a(n) for n=0..41. Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-2,-1,2,1,-1). 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) = (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]] (* A213501 *) 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 Cf. A212959. Sequence in context: A225379 A359073 A134139 * A097125 A213480 A306302 Adjacent sequences: A213498 A213499 A213500 * A213502 A213503 A213504 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 14 2012 STATUS approved

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Last modified September 21 21:57 EDT 2023. Contains 365503 sequences. (Running on oeis4.)