A213491 Number of (w,x,y) with all terms in {0,...,n} and the numbers w,x,y,|w-x|,|x-y| not distinct.

1, 8, 27, 64, 125, 204, 305, 420, 569, 714, 909, 1096, 1327, 1550, 1833, 2086, 2411, 2706, 3071, 3402, 3815, 4176, 4635, 5038, 5533, 5972, 6519, 6988, 7577, 8088, 8717, 9264, 9941, 10518, 11241, 11860, 12619, 13274, 14085, 14770, 15623

Offset: 0

Author

Clark Kimberling, Jun 13 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A212959.

Links

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

Crossrefs

Cf. A212959, A213490.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[Length[Union[{w, x, y, Abs[w - x], Abs[x - y]}]] < 5, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &,  Range[0, 60]]
(* or *)
LinearRecurrence[{0, 1, 1, 1, -1, -1, -1, 0, 1}, {1, 8, 27, 64, 125, 204, 305, 420, 569}, 60]

Formula

a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-5) - a(n-6) - a(n-7) + a(n-9).

G.f.: (1 + 8*x + 26*x^2 + 55*x^3 + 89*x^4 + 106*x^5 + 98*x^6 + 63*x^7 + 34*x^8)/(1 - x^2 - x^3 - x^4 + x^5 + x^6 + x^7 - x^9).

a(n) = (n+1)^3 - A213490(n).