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#43 by Michel Marcus at Fri Feb 18 05:16:39 EST 2022
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#42 by Hugo Pfoertner at Fri Feb 18 03:35:47 EST 2022
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#41 by Amiram Eldar at Fri Feb 18 03:28:43 EST 2022
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#40 by Amiram Eldar at Fri Feb 18 03:24:52 EST 2022
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| FORMULA
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From Amiram Eldar, Feb 18 2022: (Start)
Sum_{n>=1} 1/a(n) = 6 - sqrt(3)*Pi/2 - 2*log(2) - 3*log(3)/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi + log(2) + sqrt(3)*log(2 + sqrt(3)) - 6. (End)
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approved
editing
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#39 by Alois P. Heinz at Wed Jun 07 23:06:52 EDT 2017
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#38 by G. C. Greubel at Wed Jun 07 22:37:09 EDT 2017
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#37 by G. C. Greubel at Wed Jun 07 22:36:56 EDT 2017
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| LINKS
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G. C. Greubel, <a href="/A049453/b049453.txt">Table of n, a(n) for n = 0..1000</a>
<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
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| FORMULA
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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - G. C. Greubel, Jun 07 2017
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| MATHEMATICA
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Table[n*(6*n + 1), {n, 0, 50}] (* G. C. Greubel, Jun 07 2017 *)
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| PROG
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(PARI) x='x+O('x^50); concat([0], Vec(x*(7+5*x)/(1-x)^3)) \\ G. C. Greubel, Jun 07 2017
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approved
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#36 by Bruno Berselli at Tue Jul 28 10:09:53 EDT 2015
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#35 by Bruno Berselli at Tue Jul 28 10:09:50 EDT 2015
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| CROSSREFS
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Cf. A254963 (comment).
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approved
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#34 by Bruno Berselli at Tue Jul 28 10:05:01 EDT 2015
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