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 A212902 Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|<|x-y|<|y-z|. 2
 0, 0, 2, 14, 44, 110, 228, 426, 726, 1168, 1780, 2612, 3700, 5104, 6866, 9058, 11728, 14958, 18804, 23358, 28682, 34880, 42020, 50216, 59544, 70128, 82050, 95446, 110404, 127070, 145540, 165970, 188462, 213184, 240244, 269820, 302028 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Every term is even. For a guide to related sequences, see A211795. LINKS Index entries for linear recurrences with constant coefficients, signature (2,1,-3,-1,1,3,-1,-2,1). FORMULA a(n) = 2*a(n-1)+a(n-2)-3*a(n-3)-a(n-4)+a(n-5)+3*a(n-6)-a(n-7)-2*a(n-8)+a(n-9). G.f.: (2*x^2 + 10*x^3 + 14*x^4 + 14*x^5 + 8*x^6 + 4*x^7 )/(1 - 2*x - x^2 + 3*x^3 + x^4 - x^5 - 3*x^6 + x^7 + 2*x^8 - x^9). MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[Abs[w - x] < Abs[x - y] < Abs[y - z], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]]; m = Map[t[#] &, Range[0, 40]]   (* A212902 *) m/2 (* integers *) LinearRecurrence[{2, 1, -3, -1, 1, 3, -1, -2, 1}, {0, 0, 2, 14, 44, 110, 228, 426, 726}, 40] CROSSREFS Cf. A211795. Sequence in context: A268684 A333052 A075036 * A091405 A085929 A231247 Adjacent sequences:  A212899 A212900 A212901 * A212903 A212904 A212905 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 01 2012 STATUS approved

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Last modified December 1 11:30 EST 2021. Contains 349429 sequences. (Running on oeis4.)