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A213488 Number of (w,x,y) with all terms in {0,...,n} and |w-x|+|x-y|+|y-w| < w+x+y. 3
0, 1, 8, 27, 61, 113, 189, 295, 434, 609, 826, 1091, 1407, 1777, 2207, 2703, 3268, 3905, 4620, 5419, 6305, 7281, 8353, 9527, 10806, 12193, 13694, 15315, 17059, 18929, 20931, 23071, 25352, 27777, 30352, 33083, 35973, 39025, 42245, 45639 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n)+A213489(n)=(n+1)^3.

For a guide to related sequences, see A212959.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (4,-7,8,-7,4,-1).

FORMULA

a(n) = 4*a(n-1)-7*a(n-2)+8*a(n-3)-7*a(n-4)+4*a(n-5)-a(n-6).

G.f.: x*(1 + 4*x + 2*x^2 + x^3 + x^4)/((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] + Abs[y - w],

s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];

m = Map[t[#] &, Range[0, 60]]   (* A213488 *)

LinearRecurrence[{4, -7, 8, -7, 4, -1}, {0, 1, 8, 27, 61, 113}, 40] (* Harvey P. Dale, Sep 10 2019 *)

CROSSREFS

Cf. A212959.

Sequence in context: A131620 A141227 A224134 * A151675 A211641 A062686

Adjacent sequences:  A213485 A213486 A213487 * A213489 A213490 A213491

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 13 2012

STATUS

approved

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)