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 A212506 Number of (w,x,y,z) with all terms in {1,...,n} and w<=2x and y<=2z. 2
 0, 1, 16, 64, 196, 441, 900, 1600, 2704, 4225, 6400, 9216, 12996, 17689, 23716, 30976, 40000, 50625, 63504, 78400, 96100, 116281, 139876, 166464, 197136, 231361, 270400, 313600, 362404, 416025, 476100, 541696, 614656, 693889, 781456 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For a guide to related sequences, see A211795. LINKS Table of n, a(n) for n=0..34. Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1). FORMULA a(n) = 2a(n-1)+2a(n-2)-6a(n-3)+6a(n-5)-2a(n-6)-2a(n-7)+a(n-8). From Alois P. Heinz, May 31 2012: (Start) a(n) = A006578(n)^2. G.f.: x*(14*x+30*x^2+42*x^3+17*x^4+4*x^5+1) / ((x+1)^3*(1-x)^5). (End) MAPLE a:= n-> (n*(n+1)/2+floor(n^2/4))^2: seq(a(n), n=0..60); # Alois P. Heinz, May 31 2012 MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w <= 2 x && y <= 2 z, s = s + 1], {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]]; Map[t[#] &, Range[0, 40]] (* A212506 *) CROSSREFS Cf. A211795. Sequence in context: A316542 A306057 A059165 * A212512 A317235 A255661 Adjacent sequences: A212503 A212504 A212505 * A212507 A212508 A212509 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 19 2012 STATUS approved

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Last modified July 25 15:15 EDT 2024. Contains 374611 sequences. (Running on oeis4.)