cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A054776 a(n) = 3*n*(3*n-1)*(3*n-2).

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%I A054776 #32 Dec 21 2023 11:32:01
%S A054776 0,6,120,504,1320,2730,4896,7980,12144,17550,24360,32736,42840,54834,
%T A054776 68880,85140,103776,124950,148824,175560,205320,238266,274560,314364,
%U A054776 357840,405150,456456,511920,571704,635970,704880,778596,857280,941094
%N A054776 a(n) = 3*n*(3*n-1)*(3*n-2).
%D A054776 L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 46.
%D A054776 Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 268.
%H A054776 Konrad Knopp, <a href="http://www.hti.umich.edu/cgi/t/text/text-idx?sid=b88432273f115fb346725f1a42422e19;c=umhistmath;idno=ACM1954.0001.001">Theorie und Anwendung der unendlichen Reihen</a>, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")
%H A054776 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).
%F A054776 a(n) = A007531(3n-2) = 6*A006566(n).
%F A054776 Sum_{n>=1} 1/a(n) = Pi*sqrt(3)/12 - log(3)/4 = 0.178796768891527... [Jolley eq. 250]. - _Benoit Cloitre_, Apr 05 2002
%F A054776 G.f.: 6*x*(1+16*x+10*x^2)/(1-x)^4.
%F A054776 E.g.f.: 3*exp(x)*x*(2 + 18x + 9x^2). - _Indranil Ghosh_, Apr 15 2017
%F A054776 Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/3 - Pi/(6*sqrt(3)). - _Amiram Eldar_, Mar 08 2022
%p A054776 A054776:=n->3*n*(3*n-1)*(3*n-2): seq(A054776(n), n=0..50); # _Wesley Ivan Hurt_, Apr 14 2017
%o A054776 (PARI) a(n)=3*n*(3*n-1)*(3*n-2)
%Y A054776 Cf. A006566, A007531, A097321.
%K A054776 easy,nonn
%O A054776 0,2
%A A054776 _Henry Bottomley_, May 19 2000