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A212976
Number of (w,x,y) with all terms in {0,...,n} and odd range.
3
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.
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 03 2012
STATUS
approved