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 A114948 #44 Jan 26 2025 09:09:54
%S A114948 10,11,14,19,26,35,46,59,74,91,110,131,154,179,206,235,266,299,334,
%T A114948 371,410,451,494,539,586,635,686,739,794,851,910,971,1034,1099,1166,
%U A114948 1235,1306,1379,1454,1531,1610,1691,1774,1859,1946,2035,2126,2219,2314,2411,2510
%N A114948 a(n) = n^2 + 10.
%C A114948 Conjecture: n^2 + 10 != x^k for all n,x, and k > 1.
%C A114948 The conjecture is true: See Cohn. - _James Rayman_, Feb 14 2023
%H A114948 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 A114948 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A114948 From _Amiram Eldar_, Nov 02 2020: (Start)
%F A114948 Sum_{n>=0} 1/a(n) = (1 + sqrt(10)*Pi*coth(sqrt(10)*Pi))/20.
%F A114948 Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(10)*Pi*cosech(sqrt(10)*Pi))/20. (End)
%F A114948 From _Amiram Eldar_, Feb 12 2024: (Start)
%F A114948 Product_{n>=0} (1 - 1/a(n)) = (3/sqrt(10))*sinh(3*Pi)/sinh(sqrt(10)*Pi).
%F A114948 Product_{n>=0} (1 + 1/a(n)) = sqrt(11/10)*sinh(sqrt(11)*Pi)/sinh(sqrt(10)*Pi). (End)
%F A114948 From _Elmo R. Oliveira_, Jan 25 2025: (Start)
%F A114948 G.f.: (10 - 19*x + 11*x^2)/(1 - x)^3.
%F A114948 E.g.f.: (10 + x + x^2)*exp(x).
%F A114948 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End)
%t A114948 a[n_]:=n^2+10; a[Range[200]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 20 2011*)
%Y A114948 Cf. A114962, A114963, A114964, A114965, A241850.
%K A114948 easy,nonn
%O A114948 0,1
%A A114948 _Cino Hilliard_, Feb 21 2006
%E A114948 Edited by _Charles R Greathouse IV_, Aug 09 2010
%E A114948 a(0) = 10 prepended by _Elmo R. Oliveira_, Jan 26 2025