A213497 Number of (w,x,y) with all terms in {0,...,n} and w = min(|w-x|, |x-y|).

1, 4, 10, 17, 29, 40, 57, 73, 95, 115, 143, 167, 200, 229, 267, 300, 344, 381, 430, 472, 526, 572, 632, 682, 747, 802, 872, 931, 1007, 1070, 1151, 1219, 1305, 1377, 1469, 1545, 1642, 1723, 1825, 1910, 2018, 2107, 2220, 2314, 2432, 2530, 2654

Offset

0,2

Comments

For a guide to related sequences, see A212959.

Links

Table of n, a(n) for n=0..46.

Index entries for linear recurrences with constant coefficients, signature (0,2,1,-1,-2,0,1).

Formula

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

G.f.: (1 + 4*x + 8*x^2 + 8*x^3 + 6*x^4 + 2*x^5)/((1 - x)^3 (1 + x)^2 (1 + x + x^2)).

a(n) = (n+1)^3 - A213499(n).

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w == Min[Abs[w - x], Abs[x - y]], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]

Crossrefs

Cf. A212959, A213499.

Sequence in context: A341772 A301195 A008022 * A339576 A047699 A167209

Adjacent sequences: A213494 A213495 A213496 * A213498 A213499 A213500

Keyword

nonn,easy

Author

Clark Kimberling, Jun 14 2012

Status

approved