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 A212249 Number of (w,x,y,z) with all terms in {1,...,n} and 3w
 0, 1, 12, 63, 202, 496, 1034, 1923, 3289, 5280, 8062, 11820, 16761, 23110, 31111, 41030, 53151, 67777, 85233, 105862, 130026, 158109, 190513, 227659, 269990, 317967, 372070, 432801, 500680, 576246, 660060, 752701, 854767, 966878 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n)+A212250(n) = n^4. For a guide to related sequences, see A211795. LINKS Table of n, a(n) for n=0..33. Index entries for linear recurrences with constant coefficients, signature (4,-6,5,-5,6,-4,1). FORMULA a(n) = 4*a(n-1)-6*a(n-2)+5*a(n-3)-5*a(n-4)+6*a(n-5)-4*a(n-6)+a(n-7). G.f.: x*(1+8*x+21*x^2+17*x^3+11*x^4+x^5)/((1+x+x^2)*(1-x)^5). [Bruno Berselli, Jun 05 2012] a(n) = (59*n^4 -10*n^3 +5*n^2 -6*n -8*((((n+1) mod 3) +(-1)^((n+1) mod 3))*(-1)^(n mod 3)))/72. [Bruno Berselli, Jun 05 2012] MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[3 w < x + y + z + n, s = s + 1], {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]]; Map[t[#] &, Range[0, 40]] (* A212249 *) (* Peter J. C. Moses, Apr 13 2012 *) CROSSREFS Cf. A211795, A212247. Sequence in context: A092224 A335252 A212509 * A309372 A085463 A051922 Adjacent sequences: A212246 A212247 A212248 * A212250 A212251 A212252 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 09 2012 STATUS approved

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Last modified April 16 02:53 EDT 2024. Contains 371696 sequences. (Running on oeis4.)