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

0,2

Comments

u=average{v,w,x,y,z}. For a guide to related sequences, see A211795.

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,2,-5,10,-10,5,-1).

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

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 *)

Crossrefs

Cf. A211795, A212257, A212069.

Sequence in context: A248992 A248993 A248994 * A123005 A281227 A142477

Adjacent sequences: A212239 A212240 A212241 * A212243 A212244 A212245

Keyword

nonn

Author

Clark Kimberling, May 16 2012

Status

approved