A212242 Number of (u,v,w,x,y,z) with all terms in {0,1,...,n} and 5u=v+w+x+y+z.
1, 2, 53, 204, 625, 1556, 3357, 6558, 11809, 20000, 32211, 49762, 74263, 107564, 151875, 209716, 283967, 377918, 495219, 640000, 816821, 1030722, 1287273, 1592524, 1953125, 2376276, 2869777, 3442078, 4102229, 4860000, 5725831
Offset: 0
Keywords
Links
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,2,-5,10,-10,5,-1).
Programs
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Mathematica
t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[5 u == v + w + x + y + z, s = s + 1], {u, 0, #}, {v, 0, #},{w, 0, #}, {x, 0, #}, {y, 0, #}, {z, 0, #}] &[n]; s)]]; Map[t[#] &, Range[0, 40]] (* A212242 *) (* Peter J. C. Moses, Apr 13 2012 *) LinearRecurrence[{5,-10,10,-5,2,-5,10,-10,5,-1},{1,2,53,204,625,1556,3357,6558,11809,20000},40] (* Harvey P. Dale, Aug 20 2021 *)
Formula
a(n) = 5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+2a(n-5)-5a(n-6)+10a(n-7)-10a(n-8)+5a(n-9)-a(n-10).
G.f.: ( 1-3*x+53*x^2-51*x^3+120*x^4-51*x^5+53*x^6-3*x^7+x^8 ) / ( (x^4+x^3+x^2+x+1)*(x-1)^6 ). - R. J. Mathar, Jun 26 2012
Comments