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 A114962 #77 Nov 29 2024 19:36:19
%S A114962 14,15,18,23,30,39,50,63,78,95,114,135,158,183,210,239,270,303,338,
%T A114962 375,414,455,498,543,590,639,690,743,798,855,914,975,1038,1103,1170,
%U A114962 1239,1310,1383,1458,1535,1614,1695,1778,1863,1950,2039,2130,2223,2318,2415,2514
%N A114962 a(n) = n^2 + 14.
%C A114962 Old name was: "Numbers of the form x^2 + 14".
%C A114962 x^2 + 14 != y^n for all x,y and n > 1.
%H A114962 Vincenzo Librandi, <a href="/A114962/b114962.txt">Table of n, a(n) for n = 0..10000</a>
%H A114962 J. H. E. Cohn, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa65/aa6546.pdf">The diophantine equation x^2 + C = y^n</a>, Acta Arithmetica LXV.4 (1993).
%H A114962 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A114962 G.f.: (14-27*x+15*x^2)/(1-x)^3. - _Colin Barker_, Jan 11 2012
%F A114962 From _Amiram Eldar_, Nov 02 2020: (Start)
%F A114962 Sum_{n>=0} 1/a(n) = (1 + sqrt(14)*Pi*coth(sqrt(14)*Pi))/28.
%F A114962 Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(14)*Pi*cosech(sqrt(14)*Pi))/28. (End)
%F A114962 From _Elmo R. Oliveira_, Nov 29 2024: (Start)
%F A114962 E.g.f.: exp(x)*(14 + x + x^2).
%F A114962 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A114962 Table[n^2 + 14, {n, 0, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 15 2011 *)
%t A114962 CoefficientList[Series[(14 - 27 x + 15 x^2)/(1 - x)^3, {x, 0, 80}], x] (* _Vincenzo Librandi_, Apr 30 2014 *)
%o A114962 (Magma) [n^2+14: n in [0..60]]; // _Vincenzo Librandi_, Apr 30 2014
%Y A114962 Cf. A155136, n^2 - 28; A000290, n^2; A114948, n^2 + 10.
%Y A114962 Cf. sequences of the type n^2 + k: A002522 (k=1), A059100 (k=2), A117950 (k=3), A087475 (k=4), A117951 (k=5), A114949 (k=6), A117619 (k=7), A189833 (k=8), A189834 (k=9), A114948 (k=10), A189836 (k=11), A241748 (k=12), A241749 (k=13), this sequence (k=14), A241750 (k=15), A241751 (k=16), A241847 (k=17), A241848 (k=18), A241849 (k=19), A241850 (k=20), A241851 (k=21), A114963 (k=22), A241889 (k=23), A241890 (k=24), A114964 (k=30).
%K A114962 nonn,easy
%O A114962 0,1
%A A114962 _Cino Hilliard_, Feb 21 2006
%E A114962 Added 14 from _Vincenzo Librandi_, Apr 30 2014
%E A114962 Definition changed by _Bruno Berselli_, Mar 13 2015
%E A114962 Offset corrected by _Amiram Eldar_, Nov 02 2020