A212903 Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|<=|x-y|<=|y-z|.

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.

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (2,1,-3,-1,1,3,-1,-2,1).

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

Adjacent sequences: A212900 A212901 A212902 * A212904 A212905 A212906

Keyword

nonn,easy

Author

Clark Kimberling, Jun 01 2012

Status

approved