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A212902
Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|<|x-y|<|y-z|.
2
0, 0, 2, 14, 44, 110, 228, 426, 726, 1168, 1780, 2612, 3700, 5104, 6866, 9058, 11728, 14958, 18804, 23358, 28682, 34880, 42020, 50216, 59544, 70128, 82050, 95446, 110404, 127070, 145540, 165970, 188462, 213184, 240244, 269820, 302028
OFFSET
0,3
COMMENTS
Every term is even.
For a guide to related sequences, see A211795.
FORMULA
a(n) = 2*a(n-1)+a(n-2)-3*a(n-3)-a(n-4)+a(n-5)+3*a(n-6)-a(n-7)-2*a(n-8)+a(n-9).
G.f.: (2*x^2 + 10*x^3 + 14*x^4 + 14*x^5 + 8*x^6 + 4*x^7 )/(1 - 2*x - x^2 + 3*x^3 + x^4 - x^5 - 3*x^6 + x^7 + 2*x^8 - x^9).
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Abs[w - x] < Abs[x - y] < Abs[y - z], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 40]] (* A212902 *)
m/2 (* integers *)
LinearRecurrence[{2, 1, -3, -1, 1, 3, -1, -2, 1}, {0, 0, 2, 14, 44, 110, 228, 426, 726}, 40]
CROSSREFS
Cf. A211795.
Sequence in context: A268684 A333052 A075036 * A091405 A085929 A231247
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 01 2012
STATUS
approved