A212249 Number of (w,x,y,z) with all terms in {1,...,n} and 3w<x+y+z+n.

0, 1, 12, 63, 202, 496, 1034, 1923, 3289, 5280, 8062, 11820, 16761, 23110, 31111, 41030, 53151, 67777, 85233, 105862, 130026, 158109, 190513, 227659, 269990, 317967, 372070, 432801, 500680, 576246, 660060, 752701, 854767, 966878

Offset

0,3

Comments

a(n)+A212250(n) = n^4.

For a guide to related sequences, see A211795.

Links

Table of n, a(n) for n=0..33.

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*(1+8*x+21*x^2+17*x^3+11*x^4+x^5)/((1+x+x^2)*(1-x)^5). [Bruno Berselli, Jun 05 2012]

a(n) = (59*n^4 -10*n^3 +5*n^2 -6*n -8*((((n+1) mod 3) +(-1)^((n+1) mod 3))*(-1)^(n mod 3)))/72. [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]]  (* A212249  *)
(* Peter J. C. Moses, Apr 13 2012 *)

Crossrefs

Cf. A211795, A212247.

Sequence in context: A092224 A335252 A212509 * A309372 A085463 A051922

Adjacent sequences: A212246 A212247 A212248 * A212250 A212251 A212252

Keyword

nonn,easy

Author

Clark Kimberling, May 09 2012

Status

approved