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A079588
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a(n) = (n+1)*(2*n+1)*(4*n+1).
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5
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1, 30, 135, 364, 765, 1386, 2275, 3480, 5049, 7030, 9471, 12420, 15925, 20034, 24795, 30256, 36465, 43470, 51319, 60060, 69741, 80410, 92115, 104904, 118825, 133926, 150255, 167860, 186789, 207090, 228811, 252000, 276705, 302974, 330855, 360396, 391645
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OFFSET
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0,2
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COMMENTS
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Apart from offset, same as A100147.
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REFERENCES
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R. Tijdeman, Some applications of Diophantine approximation, pp. 261-284 of Surveys in Number Theory (Urbana, May 21, 2000), ed. M. A. Bennett et al., Peters, 2003.
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LINKS
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FORMULA
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Sum_{n>=0} 1/a(n) = Pi/3 (cf. Tijdeman).
Sum_{n>=0} a(n)/2^n = 308; Sum_{n>=0} (-1)^n*a(n)/2^n = -4/3. - L. Edson Jeffery, Mar 25 2013
Sum_{n>=0} (-1)^n/a(n) = log(2)/3 - Pi/2 + sqrt(2)*Pi/3 + 2*sqrt(2)*arcsin(1)/3. - Amiram Eldar, Jan 13 2021
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MATHEMATICA
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Table[(n + 1)*(2*n + 1)*(4*n + 1), {n, 0, 40}] (* Amiram Eldar, Jan 13 2021 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 30, 135, 364}, 40] (* Harvey P. Dale, Aug 01 2022 *)
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PROG
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(Haskell)
a079588 n = product $ map ((+ 1) . (* n)) [1, 2, 4]
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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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