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A213483 Number of (w,x,y) with all terms in {0,...,n} and |w-x|+|x-y| >= w+x+y. 3
1, 5, 13, 23, 38, 55, 78, 103, 135, 169, 211, 255, 308, 363, 428, 495, 573, 653, 745, 839, 946, 1055, 1178, 1303, 1443, 1585, 1743, 1903, 2080, 2259, 2456, 2655, 2873, 3093, 3333, 3575, 3838, 4103, 4390, 4679, 4991, 5305, 5643, 5983, 6348 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)+A213482(n) = (n+1)^3.

For a guide to related sequences, see A212959.

LINKS

Table of n, a(n) for n=0..44.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

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.: (1 + 3*x + 2*x^2 - 4*x^3 - 2*x^4 + x^5)/((1 - x)^4 (1 + x)^2)).

MATHEMATICA

t = Compile[{{n, _Integer}}, Module[{s = 0},

(Do[If[w + x + y <= Abs[w - x] + Abs[x - y], s = s + 1],

{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];

Map[t[#] &, Range[0, 60]]   (* A213483 *)

CROSSREFS

Cf. A212959.

Sequence in context: A074798 A031336 A099958 * A049833 A083800 A075829

Adjacent sequences:  A213480 A213481 A213482 * A213484 A213485 A213486

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 13 2012

STATUS

approved

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Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)