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A213481 Number of triples (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| <= w+x+y. 3
1, 7, 25, 59, 117, 202, 323, 482, 689, 945, 1261, 1637, 2085, 2604, 3207, 3892, 4673, 5547, 6529, 7615, 8821, 10142, 11595, 13174, 14897, 16757, 18773, 20937, 23269, 25760, 28431, 31272, 34305, 37519, 40937, 44547, 48373, 52402, 56659 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For a guide to related sequences, see A212959.

LINKS

Table of n, a(n) for n=0..38.

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

FORMULA

a(n) + A006918(n) = (n+1)^3.

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 + 5*x + 10*x^2 + 6*x^3 + x^4)/((1 - x)^4 (1 + x)^2)).

From Ayoub Saber Rguez, Dec 29 2021: (Start)

a(n) = A213482(n) + A213479(n).

a(n) = (23*n^3 + 66*n^2 + 64*n + 24 - (3*n+6)*(n mod 2))/24. (End)

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]]   (* A213481 *)

CROSSREFS

Cf. A212959, A213479, A213482.

Sequence in context: A268239 A350222 A110672 * A266709 A162264 A034135

Adjacent sequences:  A213478 A213479 A213480 * A213482 A213483 A213484

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 13 2012

STATUS

approved

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Last modified October 6 12:35 EDT 2022. Contains 357264 sequences. (Running on oeis4.)