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 A213399 Number of (w,x,y) with all terms in {0,...,n} and max(|w-x|,|x-y|) = x. 5
 1, 4, 14, 23, 43, 58, 88, 109, 149, 176, 226, 259, 319, 358, 428, 473, 553, 604, 694, 751, 851, 914, 1024, 1093, 1213, 1288, 1418, 1499, 1639, 1726, 1876, 1969, 2129, 2228, 2398, 2503, 2683, 2794, 2984, 3101, 3301, 3424, 3634, 3763, 3983, 4118 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For a guide to related sequences, see A212959. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5). G.f.: (1 + 3*x + 8*x^2 + 3*x^3 + x^4)/((1 - x)^3 * (1 + x)^2). From Colin Barker, Jan 26 2016: (Start) a(n) = (8*n^2+2*(-1)^n*n+8*n+(-1)^n+3)/4. a(n) = (4*n^2+5*n+2)/2 for n even. a(n) = (4*n^2+3*n+1)/2 for n odd. (End) MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[x == Max[Abs[w - x], Abs[x - y]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]]; Map[t[#] &, Range[0, 60]] (* A213399 *) PROG (PARI) Vec((1+3*x+8*x^2+3*x^3+x^4) / ((1-x)^3*(1+x)^2) + O(x^100)) \\ Colin Barker, Jan 26 2016 CROSSREFS Cf. A212959. Sequence in context: A154046 A000054 A063616 * A031254 A031224 A011534 Adjacent sequences: A213396 A213397 A213398 * A213400 A213401 A213402 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 13 2012 STATUS approved

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Last modified September 17 10:45 EDT 2024. Contains 375987 sequences. (Running on oeis4.)