A212975 Number of (w,x,y) with all terms in {0,...,n} and even range.

1, 2, 15, 28, 65, 102, 175, 248, 369, 490, 671, 852, 1105, 1358, 1695, 2032, 2465, 2898, 3439, 3980, 4641, 5302, 6095, 6888, 7825, 8762, 9855, 10948, 12209, 13470, 14911, 16352, 17985, 19618, 21455, 23292, 25345, 27398, 29679, 31960

Offset

0,2

Comments

a(n)+A212976(n) = (n+1)^3.

For a guide to related sequences, see A212959.

Links

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Formula

a(n) = (n+1)*(2*n*(n+2)+3*(-1)^n+1)/4.

a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).

G.f.: f(x)/g(x), where f(x) = 1 + 10*x^2 + x^4 and g(x) = ((1-x)^4)*(1+x)^2.

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Mod[Max[w, x, y] - Min[w, x, y], 2] == 0,
   s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]   (* A212975 *)

Crossrefs

Cf. A212959, A212976.

Sequence in context: A338457 A153080 A075312 * A128828 A032002 A071999

Adjacent sequences: A212972 A212973 A212974 * A212976 A212977 A212978

Keyword

nonn,easy

Author

Clark Kimberling, Jun 03 2012

Status

approved