A212676 Number of (w,x,y,z) with all terms in {1,...,n} and w+x=|x-y|+|y-z|.

0, 0, 1, 9, 23, 52, 92, 155, 234, 344, 475, 645, 841, 1084, 1358, 1687, 2052, 2480, 2949, 3489, 4075, 4740, 5456, 6259, 7118, 8072, 9087, 10205, 11389, 12684, 14050, 15535, 17096, 18784, 20553, 22457, 24447, 26580, 28804, 31179, 33650

Offset: 0

Author

Clark Kimberling, May 23 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, -4, 1, 2, -1).

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w + x == Abs[x - y] + Abs[y - z], s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]]   (* A212676 *)
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 0, 1, 9, 23, 52}, 41]

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^2 + 7*x^3 + 4*x^4 + x^5)/(1 - 2 x - x^2 + 4 x^3 - x^4 - 2 x^5 + x^6)