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A213045 Number of (w,x,y) with all terms in {0,...,n} and 2|w-x|>max(w,x,y)-min(w,x,y). 3
0, 4, 14, 36, 72, 128, 206, 312, 448, 620, 830, 1084, 1384, 1736, 2142, 2608, 3136, 3732, 4398, 5140, 5960, 6864, 7854, 8936, 10112, 11388, 12766, 14252, 15848, 17560, 19390, 21344, 23424, 25636, 27982, 30468, 33096, 35872, 38798, 41880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Every term is even.

a(n) + A087035(n+1) = (n+1)^3.

LINKS

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

FORMULA

a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).

G.f.: 2*x*(2 + x + x^2)/((-1 + x)^4*(1 + x)).

a(n) = 2*A212685(n+1) = (2*n*(4*n^2+9*n+8)-3*(-1)^n+3)/12. [Bruno Berselli, Jun 11 2012]

MATHEMATICA

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

(Do[If[Max[w, x, y] - Min[w, x, y] < 2 Abs[w - x],

  s = s + 1],

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

m = Map[t[#] &, Range[0, 45]]   (* A213045 *)

m/2  (* integers *)

LinearRecurrence[{3, -2, -2, 3, -1}, {0, 4, 14, 36, 72}, 50] (* Harvey P. Dale, Jul 31 2013 *)

CROSSREFS

See A212959 for a guide to related sequences.

Sequence in context: A295180 A305906 A177110 * A061989 A079908 A038164

Adjacent sequences:  A213042 A213043 A213044 * A213046 A213047 A213048

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 10 2012

STATUS

approved

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Last modified April 18 14:35 EDT 2019. Contains 322209 sequences. (Running on oeis4.)