A212577 Number of (w,x,y,z) with all terms in {1,...,n} and |w-x|=2|x-y|-|y-z|.

0, 1, 4, 17, 46, 89, 154, 251, 374, 531, 736, 979, 1268, 1621, 2024, 2485, 3026, 3629, 4302, 5071, 5914, 6839, 7876, 8999, 10216, 11561, 13004, 14553, 16246, 18049, 19970, 22051, 24254, 26587, 29096, 31739, 34524, 37501, 40624, 43901

Offset: 0

Author

Clark Kimberling, May 22 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211795.

Links

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

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Abs[w - x] == 2 Abs[x - y] - Abs[y - z],
  s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]]   (* A212577 *)
LinearRecurrence[{2, -1, 2, -4, 2, -1, 2, -1}, {0, 1, 4, 17, 46, 89, 154, 251}, 45]

Formula

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

G.f.: (x + 2*x^2 + 10*x^3 + 14*x^4 + 10*x^5 + 2*x^6 + x^7)/(1 - 2*x + x^2 - 2*x^3 + 4*x^4 - 2*x^5 + x^6 - 2*x^7 + x^8). [corrected by Georg Fischer, May 03 2019]