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 A058794 #40 Oct 31 2024 01:50:51
%S A058794 2,18,52,110,198,322,488,702,970,1298,1692,2158,2702,3330,4048,4862,
%T A058794 5778,6802,7940,9198,10582,12098,13752,15550,17498,19602,21868,24302,
%U A058794 26910,29698,32672,35838,39202,42770,46548,50542,54758,59202,63880
%N A058794 Row 3 of A007754.
%C A058794 For n >= 2, a(n) is the number of ways a triangle with side length n-1 can be completely surrounded by diamonds. See illustrations in Links. - _Craig Knecht_, Oct 08 2024
%H A058794 Seiichi Manyama, <a href="/A058794/b058794.txt">Table of n, a(n) for n = 0..10000</a>
%H A058794 Craig Knecht, <a href="/A058794/a058794.png">Number of ways a single triangle can be surrounded by diamonds</a>.
%H A058794 Craig Knecht, <a href="/A058794/a058794_1.png">The 110 ways the T2 triangle can be surrounded by diamonds</a>.
%H A058794 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A058794 a(n) = n^3 + 6*n^2 + 9*n + 2.
%F A058794 G.f.: 2*(1 + 5*x - 4*x^2 + x^3)/(1-x)^4. - _Colin Barker_, Jan 10 2012
%F A058794 a(n) = (n + 2)*(n^2 + 4*n + 1) = 2*A154560(n). - _Bruno Berselli_, Jan 10 2015
%F A058794 E.g.f.: (2 + 16*x + 9*x^2 + x^3)*exp(x). - _G. C. Greubel_, Nov 29 2018
%p A058794 seq(sum(n^2-3, k=1..n), n=2..40); # _Zerinvary Lajos_, Jan 28 2008
%p A058794 seq ((n^3)-3*n, n=2..40); # _Zerinvary Lajos_, Jun 17 2008
%t A058794 LinearRecurrence[{4,-6,4,-1}, {2,18,52,110}, 40] (* _Vladimir Joseph Stephan Orlovsky_, Jan 15 2009 *)
%t A058794 Table[n^3 + 6 n^2 + 9 n + 2, {n, 0, 40}] (* _Bruno Berselli_, Jan 10 2015 *)
%o A058794 (Magma) [n^3+6*n^2+9*n+2: n in [0..40]]; // _Vincenzo Librandi_, Sep 22 2016
%o A058794 (PARI) vector(40, n, n--; n^3+6*n^2+9*n+2) \\ _G. C. Greubel_, Nov 29 2018
%o A058794 (Sage) [(n^3+6*n^2+9*n+2) for n in range(40)] # _G. C. Greubel_, Nov 29 2018
%o A058794 (GAP) List([0..40], n -> n^3+6*n^2+9*n+2); # _G. C. Greubel_, Nov 29 2018
%Y A058794 Cf. A007754, A154560.
%K A058794 nonn,easy
%O A058794 0,1
%A A058794 _Christian G. Bower_, Dec 02 2000