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Search: id:A032765
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| A032765 |
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Floor[ n(n+1)(n+2) / n+(n+1)+(n+2) ]. |
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+0
13
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| 0, 1, 2, 5, 8, 11, 16, 21, 26, 33, 40, 47, 56, 65, 74, 85, 96, 107, 120, 133, 146, 161, 176, 191, 208, 225, 242, 261, 280, 299, 320, 341, 362, 385, 408, 431, 456, 481, 506, 533, 560, 587, 616, 645, 674, 705, 736, 767, 800, 833, 866, 901, 936, 971, 1008
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Satisfies a(n+1) -2*a(n) + a(n-1) = (2/3)(1+w^(n+1)+w^(2n+2)), a(0)=0 & a(1)=1 where w is the imaginary cubic root of unity. - Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 24 2002
First differences have this pattern: (+1) +1 +1 +3 +3 +3 +5 +5 +5 +7 +7 +7 +9 +9 +9 - Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), Dec 19 2005
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LINKS
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Eric Weisstein's World of Mathematics, Kobon Triangle
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FORMULA
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n^2 - ceil[n(n-1)/3]. G.f.: [x(1+2x^2-x^3)]/[(1+x+x^2)(1-x)^3]. - R. Stephan, May 05 2004
a(n) = Floor [n(n+2)/3]. - Saburo Tamura, sent by Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), Dec 19 2005
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MATHEMATICA
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Table[ Floor[ n(n + 1)(n + 2)/(n + (n + 1) + (n + 2))], {n, 0, 55}]
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CROSSREFS
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Cf. A001082, A032766.
Sequence in context: A118518 A088366 A130258 this_sequence A129300 A107679 A018846
Adjacent sequences: A032762 A032763 A032764 this_sequence A032766 A032767 A032768
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KEYWORD
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nonn
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com), May 15, 1998.
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