A212976 Number of (w,x,y) with all terms in {0,...,n} and odd range.

0, 6, 12, 36, 60, 114, 168, 264, 360, 510, 660, 876, 1092, 1386, 1680, 2064, 2448, 2934, 3420, 4020, 4620, 5346, 6072, 6936, 7800, 8814, 9828, 11004, 12180, 13530, 14880, 16416, 17952, 19686, 21420, 23364, 25308, 27474, 29640, 32040

Offset

0,2

Comments

a(n) + A212975(n) = (n+1)^3. Six divides every term.

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) = 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) = 6*x*(1 + x^2) and g(x) = ((1-x)^4)*(1+x)^2.

a(n+1) = 6*A005993(n). [Bruno Berselli, Jun 15 2012]

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Mod[Max[w, x, y] - Min[w, x, y], 2] == 1,
   s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]   (* A212976 *)
m/6  (* A005993 except for initial 0 *)
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 6, 12, 36, 60, 114}, 40] (* Harvey P. Dale, Jan 21 2017 *)

Crossrefs

Cf. A005993, A212959, A212975.

Sequence in context: A306899 A096932 A376003 * A352621 A176681 A064476

Adjacent sequences: A212973 A212974 A212975 * A212977 A212978 A212979

Keyword

nonn,easy

Author

Clark Kimberling, Jun 03 2012

Status

approved