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.

A085377 a(n) = 15n^2 + 13n^3.

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%I A085377 #13 Mar 30 2012 17:38:51
%S A085377 0,28,164,486,1072,2000,3348,5194,7616,10692,14500,19118,24624,31096,
%T A085377 38612,47250,57088,68204,80676,94582,110000,127008,145684,166106,
%U A085377 188352,212500,238628,266814,297136,329672,364500,401698,441344,483516,528292
%N A085377 a(n) = 15n^2 + 13n^3.
%C A085377 Numbers that are the sum of three solutions of the Diophantine equation x^3 - y^3 = z^2.
%C A085377 Parametric representation of the solution is (x,y,z) = (8n^2, 7n^2, 13n^3), thus getting a(n) = 8n^2 + 7n^2 + 13n^3 = 15n^2 + 13n^3.
%C A085377 Geometrically, 13^2 = 8^3 - 7^3 means that the square of the hypotenuse of a Pythagorean triangle (5,12,13) is the difference of two cubes, which I recently found on p70 of David Wells' book "The Penguin Dictionary of Curios and Interesting Numbers", Penguin Books, 1997. See also A085479.
%F A085377 a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: 2*x*(14+26*x-x^2)/(1-x)^4. [From _R. J. Mathar_, Apr 20 2009]
%t A085377 Table[15n^2 + 13n^3, {n, 1, 34}]
%Y A085377 Cf. A085409.
%K A085377 nonn
%O A085377 0,2
%A A085377 Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Aug 12 2003
%E A085377 More terms from _Robert G. Wilson v_, Aug 16 2003
%E A085377 Edited by _N. J. A. Sloane_, Apr 29 2008