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.
%I A058919 #49 Dec 29 2024 21:01:26
%S A058919 1,1,5,25,85,221,481,925,1625,2665,4141,6161,8845,12325,16745,22261,
%T A058919 29041,37265,47125,58825,72581,88621,107185,128525,152905,180601,
%U A058919 211901,247105,286525,330485,379321,433381,493025,558625,630565,709241,795061,888445,989825,1099645
%N A058919 a(n) = n^4/2 - n^3 + 3*n^2/2 - n + 1 = (n^2 + 1)*(n^2 - 2*n + 2)/2.
%C A058919 On an n X (n - 1)(n - 2)/2 X n(n - 1)/2 cuboid with n >= 5, the two points at greatest surface distance from a corner are the opposite corner and the point 1 in from each of the two edges on a smallest face which meet at the opposite corner; this greatest surface distance is sqrt(a(n)).
%C A058919 Subsequence of A080827, see formula. - _David James Sycamore_, Jul 31 2018
%H A058919 Harry J. Smith, <a href="/A058919/b058919.txt">Table of n, a(n) for n = 0..500</a>
%H A058919 Henry Bottomley, <a href="http://se16.info/js/cuboid.htm#Numerical">Source</a>
%H A058919 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A058919 G.f.: (1 - 4*x + 10*x^2 + 5*x^4)/(1 - x)^5. - _Colin Barker_, Jan 01 2012
%F A058919 a(n) = A002522(n)*A002522(n-1)/2, with A002522(-1)=2. - _Bruno Berselli_, Nov 11 2014
%F A058919 a(n) = A080827(n^2-n+1). - _David James Sycamore_, Jul 31 2018
%F A058919 E.g.f.: exp(x)*(2 + 4*x^2 + 4*x^3 + x^4)/2. - _Stefano Spezia_, Oct 08 2022
%F A058919 For n>1, a(n) = A000217(n-1)^2 + (A000217(n-1)+1)^2 = (A000217(n)-1)^2 + (A000217(n-2)-1)^2. - _Charlie Marion_, Feb 08 2024
%p A058919 A058919:=n->n^4/2 - n^3 + 3*n^2/2 - n + 1; seq(A058919(n), n=0..30); # _Wesley Ivan Hurt_, May 10 2014
%t A058919 Table[n^4/2 - n^3 + 3 n^2/2 - n + 1, {n, 0, 30}] (* _Wesley Ivan Hurt_, May 10 2014 *)
%o A058919 (PARI) a(n) = { (n^4 + 3*n^2)/2 - n^3 - n + 1 } \\ _Harry J. Smith_, Jun 23 2009
%o A058919 (Magma) [n^4/2 - n^3 + 3*n^2/2 - n + 1: n in [0..30]]; // _Wesley Ivan Hurt_, May 10 2014
%Y A058919 For n >= 4 the sequence is a subsequence of A007692.
%Y A058919 Cf. A002522, A080827.
%K A058919 nonn,easy
%O A058919 0,3
%A A058919 _Henry Bottomley_, Jan 11 2001