A114948 a(n) = n^2 + 10.
10, 11, 14, 19, 26, 35, 46, 59, 74, 91, 110, 131, 154, 179, 206, 235, 266, 299, 334, 371, 410, 451, 494, 539, 586, 635, 686, 739, 794, 851, 910, 971, 1034, 1099, 1166, 1235, 1306, 1379, 1454, 1531, 1610, 1691, 1774, 1859, 1946, 2035, 2126, 2219, 2314, 2411, 2510
Offset: 0
Links
- J. H. E. Cohn, The diophantine equation x^2 + C = y^n, Acta Arithmetica LXV.4 (1993).
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Mathematica
a[n_]:=n^2+10; a[Range[200]] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2011*)
Formula
From Amiram Eldar, Nov 02 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(10)*Pi*coth(sqrt(10)*Pi))/20.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(10)*Pi*cosech(sqrt(10)*Pi))/20. (End)
From Amiram Eldar, Feb 12 2024: (Start)
Product_{n>=0} (1 - 1/a(n)) = (3/sqrt(10))*sinh(3*Pi)/sinh(sqrt(10)*Pi).
Product_{n>=0} (1 + 1/a(n)) = sqrt(11/10)*sinh(sqrt(11)*Pi)/sinh(sqrt(10)*Pi). (End)
From Elmo R. Oliveira, Jan 25 2025: (Start)
G.f.: (10 - 19*x + 11*x^2)/(1 - x)^3.
E.g.f.: (10 + x + x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End)
Extensions
Edited by Charles R Greathouse IV, Aug 09 2010
a(0) = 10 prepended by Elmo R. Oliveira, Jan 26 2025
Comments