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

0,2

Comments

For a guide to related sequences, see A212959.

Links

Table of n, a(n) for n=0..40.

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

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).

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]

Crossrefs

Cf. A212959, A213490.

Sequence in context: A017670 A353621 A126200 * A276919 A076989 A270437

Adjacent sequences: A213488 A213489 A213490 * A213492 A213493 A213494

Keyword

nonn,easy

Author

Clark Kimberling, Jun 13 2012

Status

approved