A213499 Number of (w,x,y) with all terms in {0,...,n} and w != min(|w-x|, |x-y|).

0, 4, 17, 47, 96, 176, 286, 439, 634, 885, 1188, 1561, 1997, 2515, 3108, 3796, 4569, 5451, 6429, 7528, 8735, 10076, 11535, 13142, 14878, 16774, 18811, 21021, 23382, 25930, 28640, 31549, 34632, 37927, 41406, 45111, 49011, 53149, 57494

Offset

0,2

Comments

For a guide to related sequences, see A212959.

Links

Table of n, a(n) for n=0..38.

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

Formula

a(n) = a(n-1) + 2*a(n-2) - a(n-3) - 2*a(n-4) - a(n-5) + 2*a(n-6) + a(n-7) - a(n-8).

G.f.: (x*(4 + 13*x + 22*x^2 + 19*x^3 + 11*x^4 + 3*x^5))/((-1 + x)^4 (1 + x)^2 (1 + x + x^2)).

a(n) = (n+1)^3 - A213497(n).

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w != Min[Abs[w - x], Abs[x - y]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]
LinearRecurrence[{1, 2, -1, -2, -1, 2, 1, -1}, {0, 4, 17, 47, 96, 176, 286, 439}, 40] (* or *) CoefficientList[Series[(x (4+13 x+22 x^2+19 x^3+11 x^4+3 x^5))/((-1+x)^4 (1+x)^2 (1+x+x^2)), {x, 0, 40}], x] (* Harvey P. Dale, Sep 03 2021 *)

Crossrefs

Cf. A212959, A213497.

Sequence in context: A212577 A332863 A119949 * A213502 A273334 A273766

Adjacent sequences: A213496 A213497 A213498 * A213500 A213501 A213502

Keyword

nonn,easy

Author

Clark Kimberling, Jun 14 2012

Status

approved