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A212090
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Number of (w,x,y,z) with all terms in {1,...,n} and w<x+y+z.
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2
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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
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OFFSET
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0,3
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COMMENTS
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a(n)+A000332(n+1) = n^4. For a guide to related sequences, see A211795.
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LINKS
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FORMULA
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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.
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MATHEMATICA
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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[%]
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 16, 80, 251}, 34] (* Ray Chandler, Aug 02 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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