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 A212250 Number of (w,x,y,z) with all terms in {1,...,n} and 3w>=x+y+z+n. 3
 0, 0, 4, 18, 54, 129, 262, 478, 807, 1281, 1938, 2821, 3975, 5451, 7305, 9595, 12385, 15744, 19743, 24459, 29974, 36372, 43743, 52182, 61786, 72658, 84906, 98640, 113976, 131035, 149940, 170820, 193809, 219043, 246664, 276819, 309657 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n)+A212249 = n^4. For a guide to related sequences, see A211795. LINKS Table of n, a(n) for n=0..36. 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^2*(4+2*x+6*x^2+x^3)/((1+x+x^2)*(1-x)^5). [Bruno Berselli, Jun 05 2012] a(n) = (13*n^4+10*n^3-5*n^2+6*n+8*b)/72, where b = 0,-3,1,0,-3,1,... (repeated). [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]] (* A212250 *) (* Peter J. C. Moses, Apr 13 2012 *) CROSSREFS Cf. A211795, A212247, A212249. Sequence in context: A320544 A020644 A182031 * A229788 A242206 A181411 Adjacent sequences: A212247 A212248 A212249 * A212251 A212252 A212253 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 09 2012 STATUS approved

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Last modified August 3 05:44 EDT 2024. Contains 374875 sequences. (Running on oeis4.)