A212679 Number of (w,x,y,z) with all terms in {1,...,n} and |x-y|=|y-z|.

0, 1, 8, 33, 80, 165, 288, 469, 704, 1017, 1400, 1881, 2448, 3133, 3920, 4845, 5888, 7089, 8424, 9937, 11600, 13461, 15488, 17733, 20160, 22825, 25688, 28809, 32144, 35757, 39600, 43741, 48128, 52833, 57800, 63105, 68688, 74629, 80864

Offset

0,3

Comments

For a guide to related sequences, see A211795.

Links

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

Index entries for linear recurrences with constant coefficients, signature (2, 1, -4, 1, 2, -1).

Formula

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

G.f.: (x + 6*x^2 + 16*x^3 + 10*x^4 + 3*x^5)/(1 - 2*x - x^2 + 4*x^3 - x^4 - 2*x^5 + x^6)

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Abs[x - y] == Abs[y - z], s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]]   (* A212679 *)
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 1, 8, 33, 80, 165}, 50]

Crossrefs

Cf. A211795.

Sequence in context: A044466 A022274 A118312 * A204468 A140867 A212133

Adjacent sequences: A212676 A212677 A212678 * A212680 A212681 A212682

Keyword

nonn,easy

Author

Clark Kimberling, May 23 2012

Status

approved