A117619 a(n) = n^2 + 7.
7, 8, 11, 16, 23, 32, 43, 56, 71, 88, 107, 128, 151, 176, 203, 232, 263, 296, 331, 368, 407, 448, 491, 536, 583, 632, 683, 736, 791, 848, 907, 968, 1031, 1096, 1163, 1232, 1303, 1376, 1451, 1528, 1607, 1688, 1771, 1856, 1943, 2032, 2123, 2216, 2311, 2408, 2507
Offset: 0
Links
- Ivan Panchenko, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Mathematica
Table[n^2 + 7, {n, 0, 60}] (* Stefan Steinerberger, Apr 08 2006 *) -
PARI
a(n) = n^2 + 7 \\ Indranil Ghosh, Apr 05 2017
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Python
def a(n): return n**2 + 7 # Indranil Ghosh, Apr 05 2017
Formula
G.f.: (-8*x^2 + 13*x - 7)/(x - 1)^3. - Indranil Ghosh, Apr 05 2017
From Amiram Eldar, Nov 02 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(7)*Pi*coth(sqrt(7)*Pi))/14.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(7)*Pi*cosech(sqrt(7)*Pi))/14. (End)
From Amiram Eldar, Feb 05 2024: (Start)
Product_{n>=0} (1 - 1/a(n)) = sqrt(6/7)*sinh(sqrt(6)*Pi)/sinh(sqrt(7)*Pi).
Product_{n>=0} (1 + 1/a(n)) = 2*sqrt(2/7)*sinh(2*sqrt(2)*Pi)/sinh(sqrt(7)*Pi). (End)
From Elmo R. Oliveira, Nov 29 2024: (Start)
E.g.f.: exp(x)*(7 + x + x^2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
Extensions
More terms from Stefan Steinerberger, Apr 08 2006