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A058212
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1 + floor(n*(n-3)/6).
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3
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1, 0, 0, 1, 1, 2, 4, 5, 7, 10, 12, 15, 19, 22, 26, 31, 35, 40, 46, 51, 57, 64, 70, 77, 85, 92, 100, 109, 117, 126, 136, 145, 155, 166, 176, 187, 199, 210, 222, 235, 247, 260, 274, 287, 301, 316, 330, 345, 361, 376, 392, 409, 425, 442, 460, 477
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| For n >= 3, number of solutions to x+y+z=0 (mod n) with 0<=x<y<z<n. E.g. for n=3 there is a unique solution, x=0, y=1, z=2.
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LINKS
| S. A. Burr, B. Gr\"{u}nbaum and N. J. A. Sloane, The Orchard Problem, Geometriae Dedicata, 2 (1974), 397-424.
Index to sequences with linear recurrences with constant coefficients, signature (2,-1,1,-2,1)
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FORMULA
| G.f.: (1-2x+x^2+x^4)/((1-x)^2(1-x^3)); a(n)=4cos(2*pi*n/3)/9+(3n^2-9n+10)/18. - Paul Barry (pbarry(AT)wit.ie), Mar 18 2004
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PROG
| (Other) sage: [ceil(binomial(n, 2)/3) for n in xrange(-1, 55)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 03 2009]
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CROSSREFS
| Cf. A003035, A007997.
Apart from initial term, same as A007997.
The third diagonal of A061857 ?
Sequence in context: A188468 A092311 A186386 * A007997 A123120 A194462
Adjacent sequences: A058209 A058210 A058211 * A058213 A058214 A058215
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 30 2000
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EXTENSIONS
| Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 07 2009
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