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A212903
Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|<=|x-y|<=|y-z|.
2
1, 8, 35, 94, 209, 398, 697, 1130, 1743, 2568, 3661, 5060, 6833, 9024, 11711, 14946, 18817, 23382, 28741, 34958, 42143, 50368, 59753, 70376, 82369, 95816, 110859, 127590, 146161, 166670, 189281, 214098, 241295, 270984, 303349, 338508
OFFSET
0,2
COMMENTS
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.: (1 + 6*x + 18*x^2 + 19*x^3 + 11*x^4 - 2*x^5 - 2*x^6 + 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]] (* A212903 *)
LinearRecurrence[{2, 1, -3, -1, 1, 3, -1, -2, 1}, {1, 8, 35, 94, 209, 398, 697, 1130, 1743}, 40]
CROSSREFS
Cf. A211795.
Sequence in context: A100907 A303383 A265840 * A168566 A058102 A212674
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 01 2012
STATUS
approved