A212579 Number of (w,x,y,z) with all terms in {1,...,n} and min{|w-x|,|w-y|}=min{|x-y|,|x-z|}.

0, 1, 8, 31, 80, 171, 308, 509, 780, 1137, 1584, 2143, 2812, 3615, 4552, 5645, 6892, 8321, 9924, 11731, 13736, 15967, 18416, 21117, 24056, 27269, 30744, 34515, 38568, 42943, 47620, 52641, 57988, 63701, 69760, 76211, 83028, 90259, 97880

Offset

0,3

Comments

For a guide to related sequences, see A211795.

Links

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

Bertrand Teguia Tabuguia, Hypergeometric-Type Sequences, arXiv:2401.00256 [cs.SC], 2023.

Bertrand Teguia Tabuguia, Computing with Hypergeometric-Type Terms, arXiv:2404.10143 [cs.SC], 2024.

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 + 7*x^2 + 21*x^3 + 34*x^4 + 39*x^5 + 25*x^6 + 7*x^7)/(1 - x - 2* x^2 + x^3 + 2*x^4 + x^5 - 2*x^6 - x^7 + x^8).

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Min[Abs[w - x], Abs[w - y]] == Min[Abs[x - y], Abs[x - z]],
s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]]   (* A212579 *)
LinearRecurrence[{1, 2, -1, -2, -1, 2, 1, -1}, {0, 1, 8, 31, 80, 171, 308, 509}, 50]

Crossrefs

Cf. A211795.

Sequence in context: A061294 A240707 A115293 * A115004 A303522 A299261

Adjacent sequences: A212576 A212577 A212578 * A212580 A212581 A212582

Keyword

nonn,easy

Author

Clark Kimberling, May 22 2012

Status

approved