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 A212509 Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y<=3z. 4
 0, 1, 12, 63, 180, 437, 891, 1628, 2736, 4392, 6600, 9646, 13608, 18669, 24990, 32955, 42432, 54033, 67797, 84010, 102900, 125118, 150282, 179444, 212544, 249977, 292032, 339687, 392196, 451165, 516375, 588336, 667392, 754908, 849660, 953922, 1067256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For a guide to related sequences, see A211795. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,2,2,-1,-4,0,2,0,-2,0,4,1,-2,-2,0,1). FORMULA a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)+2*a(n-7)-2*a(n-9)+4*a(n-11)+a(n-12)-2*a(n-13)-2*a(n-14)+a(n-16). G.f.: x*(1 +12*x +61*x^2 +154*x^3 +288*x^4 +421*x^5 +505*x^6 +510*x^7 +487*x^8 +387*x^9 +246*x^10 +120*x^11 +42*x^12 +6*x^13) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - Colin Barker, Dec 17 2015 MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w < 2 x && y <= 3 z, s = s + 1], {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]]; Map[t[#] &, Range[0, 50]] (* A212509 *) PROG (PARI) concat(0, Vec(x*(1 +12*x +61*x^2 +154*x^3 +288*x^4 +421*x^5 +505*x^6 +510*x^7 +487*x^8 +387*x^9 +246*x^10 +120*x^11 +42*x^12 +6*x^13) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^60))) \\ Colin Barker, Dec 17 2015 CROSSREFS Cf. A211795, A212508. Sequence in context: A349159 A092224 A335252 * A212249 A309372 A085463 Adjacent sequences: A212506 A212507 A212508 * A212510 A212511 A212512 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 20 2012 STATUS approved

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Last modified April 19 19:02 EDT 2024. Contains 371798 sequences. (Running on oeis4.)