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 A213497 Number of (w,x,y) with all terms in {0,...,n} and w = min(|w-x|,|x-y|) 3
 1, 4, 10, 17, 29, 40, 57, 73, 95, 115, 143, 167, 200, 229, 267, 300, 344, 381, 430, 472, 526, 572, 632, 682, 747, 802, 872, 931, 1007, 1070, 1151, 1219, 1305, 1377, 1469, 1545, 1642, 1723, 1825, 1910, 2018, 2107, 2220, 2314, 2432, 2530, 2654 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n)+A213499(n) = (n+1)^3. For a guide to related sequences, see A212959. LINKS Index entries for linear recurrences with constant coefficients, signature (0,2,1,-1,-2,0,1). FORMULA a(n) = 2*a(n-2)+a(n-3)-a(n-4)-2*a(n-5)+a(n-7). G.f.: (1 + 4*x + 8*x^2 + 8*x^3 + 6*x^4 + 2*x^5)/((1 - x)^3 (1 + x)^2 (1 + x + x^2)). MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w == Min[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]]   (* A213497 *) CROSSREFS Cf. A212959. Sequence in context: A213398 A002442 A008022 * A047699 A167209 A096077 Adjacent sequences:  A213494 A213495 A213496 * A213498 A213499 A213500 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 14 2012 STATUS approved

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