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A111384
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Binomial(n,3) - binomial(floor(n/2),3) - binomial(ceiling(n/2),3).
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3
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0, 0, 0, 1, 4, 9, 18, 30, 48, 70, 100, 135, 180, 231, 294, 364, 448, 540, 648, 765, 900, 1045, 1210, 1386, 1584, 1794, 2028, 2275, 2548, 2835, 3150, 3480, 3840, 4216, 4624, 5049, 5508, 5985, 6498, 7030, 7600, 8190, 8820, 9471, 10164, 10879, 11638, 12420, 13248
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| a(n) is also floor(n/2)*ceiling(n/2)*(n-2)/2 [From James Buddenhagen (jbuddenh(AT)gmail.com), Nov 11 2009]
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 03 2010: (Start)
Starting with 1 = M * [1, 2, 3,...] where M = a matrix with (1, 4, 7, 10,...)
in every column, shifted down twice for columns >1. The row sums of triangle
M = A006578: (1, 4, 8, 14, 21, 30, 40,...). (End)
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REFERENCES
| P. Keevash et al., The Turan number of the Fano plane, Combinatorica, 25 (2005), 561-574.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).
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FORMULA
| 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. x^3*(1+2*x)/ ((1+x)^2 * (x-1)^4). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 18 2010]
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MAPLE
| seq(floor(n/2)*ceil(n/2)*(n-2)/2, n=0..50); [From James Buddenhagen (jbuddenh(AT)gmail.com), Nov 11 2009]
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CROSSREFS
| Cf. A006578 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 03 2010]
Sequence in context: A008020 A008146 A038098 * A196039 A008219 A008223
Adjacent sequences: A111381 A111382 A111383 * A111385 A111386 A111387
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 10 2005
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