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 A212090 Number of (w,x,y,z) with all terms in {1,...,n} and w
 0, 1, 16, 80, 251, 610, 1261, 2331, 3970, 6351, 9670, 14146, 20021, 27560, 37051, 48805, 63156, 80461, 101100, 125476, 154015, 187166, 225401, 269215, 319126, 375675, 439426, 510966, 590905, 679876, 778535, 887561, 1007656, 1139545 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n)+A000332(n+1) = n^4. For a guide to related sequences, see A211795. LINKS Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1). FORMULA a(n) = 5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+a(n-5). G.f.: -x*(1+11*x+10*x^2+x^3) / (x-1)^5. a(n) = n*(-2+(1+(2+23*n)*n)*n)/24. MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w < x + y + z, s = s + 1], {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]]; Map[t[#] &, Range[0, 50]] (* A212090 *) FindLinearRecurrence[%] (* Peter J. C. Moses, Apr 13 2012 *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 16, 80, 251}, 34] (* Ray Chandler, Aug 02 2015 *) CROSSREFS Cf. A211795, A212091. Sequence in context: A271992 A008511 A130810 * A212240 A050468 A242167 Adjacent sequences:  A212087 A212088 A212089 * A212091 A212092 A212093 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 01 2012 STATUS approved

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Last modified July 26 10:21 EDT 2021. Contains 346294 sequences. (Running on oeis4.)