A212674 Number of (w,x,y,z) with all terms in {1,...,n} and w > |x-y| + |y-z|.

0, 1, 8, 35, 104, 247, 504, 925, 1568, 2501, 3800, 5551, 7848, 10795, 14504, 19097, 24704, 31465, 39528, 49051, 60200, 73151, 88088, 105205, 124704, 146797, 171704, 199655, 230888, 265651, 304200, 346801, 393728, 445265, 501704

Offset

0,3

Comments

a(n)+A212673(n) = n^4. For a guide to related sequences, see A211795.

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (4, -5, 0, 5, -4, 1).

Formula

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

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

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w > Abs[x - y] + Abs[y - z], s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]]   (* A212674 *)
LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 1, 8, 35, 104, 247}, 40]

Crossrefs

Cf. A211795.

Sequence in context: A212903 A168566 A058102 * A279743 A189592 A285737

Adjacent sequences: A212671 A212672 A212673 * A212675 A212676 A212677

Keyword

nonn,easy

Author

Clark Kimberling, May 23 2012

Status

approved