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A241850 a(n) = n^2 + 20. 4
20, 21, 24, 29, 36, 45, 56, 69, 84, 101, 120, 141, 164, 189, 216, 245, 276, 309, 344, 381, 420, 461, 504, 549, 596, 645, 696, 749, 804, 861, 920, 981, 1044, 1109, 1176, 1245, 1316, 1389, 1464, 1541, 1620, 1701, 1784, 1869, 1956, 2045, 2136, 2229, 2324 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The only solution for x at the Diophantine equation x^2 + 20 = y^m (with m>2) is 14: 14^2 + 20 = a(14) = 6^3. - Bruno Berselli, May 01 2014
LINKS
J. H. E. Cohn, The diophantine equation x^2 + C = y^n, Acta Arithmetica LXV.4, 1993, p. 379.
FORMULA
G.f.: (20 - 39*x + 21*x^2)/(1 - x)^3.
a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 2*n - 1.
From Amiram Eldar, Nov 03 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(20)*Pi*coth(sqrt(20)*Pi))/40.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(20)*Pi*cosech(sqrt(20)*Pi))/40. (End)
MATHEMATICA
Table[n^2 + 20, {n, 0, 60}]
PROG
(Magma) [n^2+20: n in [0..60]];
(PARI) a(n)=n^2+20 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. similar sequences listed in A114962.
Sequence in context: A347469 A030605 A125663 * A138601 A278582 A218539
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, May 01 2014
STATUS
approved

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Last modified March 4 16:13 EST 2024. Contains 370532 sequences. (Running on oeis4.)