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 A134593 #52 Sep 27 2024 05:40:32
%S A134593 1,16,41,76,121,176,241,316,401,496,601,716,841,976,1121,1276,1441,
%T A134593 1616,1801,1996,2201,2416,2641,2876,3121,3376,3641,3916,4201,4496,
%U A134593 4801,5116,5441,5776,6121,6476,6841,7216,7601,7996,8401,8816,9241,9676,10121
%N A134593 a(n) = 5*n^2 + 10*n + 1. Coefficients of the rational part of (1 + sqrt(n))^5.
%C A134593 (1+sqrt(n))^5 = (5*n^2 + 10*n + 1) + (n^2 + 10*n + 5)*sqrt(n). Coefficients of the irrational part are A134594.
%C A134593 Number of entries required to describe the options and constraints in Don Knuth's formulation of the n nonattacking queens on an n X n board problem (A000170) as input for his DLX (Dancing Links eXact coverage) program. Can be seen as "entries successfully read" in the video from his 2018 Annual Christmas Lecture. - _Hugo Pfoertner_, Jan 09 2019
%H A134593 D. E. Knuth, <a href="https://youtu.be/_cR9zDlvP88?t=3177">Donald Knuth's 24th Annual Christmas Lecture: Dancing Links</a>, Stanfordonline, Video published on YouTube, Dec 12, 2018.
%H A134593 Takao Komatsu, Ritika Goel, and Neha Gupta, <a href="https://arxiv.org/abs/2409.14788">The Frobenius number for the triple of the 2-step star numbers</a>, arXiv:2409.14788 [math.CO], 2024. See p. 2.
%H A134593 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A134593 G.f.: (4*x^2 - 13*x - 1)/(x-1)^3. - _R. J. Mathar_, Nov 14 2007
%F A134593 a(n) = a(n-1) + 10*n + 5 (with a(0)=1). - _Vincenzo Librandi_, Nov 23 2010
%F A134593 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Wesley Ivan Hurt_, May 17 2021
%F A134593 E.g.f.: exp(x)*(1 + 15*x + 5*x^2). - _Stefano Spezia_, Sep 27 2024
%t A134593 Table[(5n^2 + 10n + 1), {n, 0, 50}]
%t A134593 LinearRecurrence[{3,-3,1},{1,16,41},50] (* _Harvey P. Dale_, Oct 20 2023 *)
%o A134593 (Python)
%o A134593 print([5*i**2-4 for i in range(1,100)])
%o A134593 # _Ruskin Harding_, Mar 27 2013
%o A134593 (PARI) a(n)=5*n^2+10*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A134593 Cf. A000170, A134594.
%K A134593 nonn,easy
%O A134593 0,2
%A A134593 _Artur Jasinski_, Nov 04 2007
%E A134593 Edited by _Charles R Greathouse IV_, Aug 09 2010