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A212145
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Number of (w,x,y,z) with all terms in {1,...,n} and w<2x+y+z.
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2
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0, 1, 16, 81, 255, 621, 1285, 2377, 4050, 6481, 9870, 14441, 20441, 28141, 37835, 49841, 64500, 82177, 103260, 128161, 157315, 191181, 230241, 275001, 325990, 383761, 448890, 521977, 603645, 694541, 795335, 906721, 1029416, 1164161
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = 4*a(n-1)-5*a(n-2)+5*a(n-4)-4*a(n-5)+a(n-6).
a(n) = (3-3*(-1)^n-8*n-4*n^2+8*n^3+94*n^4)/96. - Colin Barker, Nov 21 2014
G.f.: -x*(x^4+11*x^3+22*x^2+12*x+1) / ((x-1)^5*(x+1)). - Colin Barker, Nov 21 2014
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MAPLE
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MATHEMATICA
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t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w < 2 x + y + z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 60]] (* A212145 *)
FindLinearRecurrence[%]
CoefficientList[Series[x (x^4 + 11 x^3 + 22 x^2 + 12 x + 1) / ((1 - x)^5 (x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 22 2014 *)
LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 1, 16, 81, 255, 621}, 34] (* Ray Chandler, Aug 02 2015 *)
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PROG
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(PARI) concat(0, Vec(-x*(x^4+11*x^3+22*x^2+12*x+1)/((x-1)^5*(x+1)) + O(x^100))) \\ Colin Barker, Nov 21 2014
(Magma) [(3-3*(-1)^n-8*n-4*n^2+8*n^3+94*n^4)/96 : n in [0..40]]; // Wesley Ivan Hurt, Nov 21 2014
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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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