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A067046
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a(n) = lcm(n, n+1, n+2)/6.
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7
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1, 2, 10, 10, 35, 28, 84, 60, 165, 110, 286, 182, 455, 280, 680, 408, 969, 570, 1330, 770, 1771, 1012, 2300, 1300, 2925, 1638, 3654, 2030, 4495, 2480, 5456, 2992, 6545, 3570, 7770, 4218, 9139, 4940, 10660, 5740, 12341, 6622, 14190, 7590, 16215, 8648, 18424, 9800
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: (x^4 + 2x^3 + 6x^2 + 2x + 1)/(1 - x^2)^4.
a(n) = binomial(n+2,3)*(3-(-1)^n)/4. - Gary Detlefs, Apr 13 2011
Quasipolynomial: a(n) = n(n+1)(n+2)/6 when n is odd and n(n+1)(n+2)/12 otherwise. - Charles R Greathouse IV, Feb 27 2012
Sum_{n>=1} 1/a(n) = 6*(1 - log(2)).
Sum_{n>=1} (-1)^(n+1)/a(n) = 6*(3*log(2) - 2). (End)
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EXAMPLE
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a(6) = 28 as lcm(6,7,8)/6 = 168/6 = 28.
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MATHEMATICA
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PROG
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(PARI) { for (n=1, 1000, write("b067046.txt", n, " ", lcm(lcm(n, n+1), n+2)/6) ) } \\ Harry J. Smith, Apr 30 2010
(Haskell)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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