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A212960 Number of (w,x,y) with all terms in {0,...,n} and |w-x| != |x-y|. 2
0, 4, 16, 44, 92, 168, 276, 424, 616, 860, 1160, 1524, 1956, 2464, 3052, 3728, 4496, 5364, 6336, 7420, 8620, 9944, 11396, 12984, 14712, 16588, 18616, 20804, 23156, 25680, 28380, 31264, 34336, 37604, 41072, 44748, 48636, 52744, 57076 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)+A212959(n)=(n+1)^3.  Every term is divisible by 4.

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 (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.: f(x)/g(x), where f(x)=4x(1+x^2+x^3) and g(x)=(1+x)(1-x)^4.

a(n) = (4*n^3 + 6*n^2 + 4*n+1 - (-1)^n)/4. - Luce ETIENNE, Apr 05 2014

MATHEMATICA

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

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

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

m = Map[t[#] &, Range[0, 45]]   (* A212960 *)

m/4 (* integers *)

CROSSREFS

Cf. A212959.

Sequence in context: A183536 A161142 A259013 * A217873 A289086 A018210

Adjacent sequences:  A212957 A212958 A212959 * A212961 A212962 A212963

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 01 2012

STATUS

approved

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Last modified October 23 20:58 EDT 2018. Contains 316533 sequences. (Running on oeis4.)