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 A241849 a(n) = n^2 + 19. 2
 19, 20, 23, 28, 35, 44, 55, 68, 83, 100, 119, 140, 163, 188, 215, 244, 275, 308, 343, 380, 419, 460, 503, 548, 595, 644, 695, 748, 803, 860, 919, 980, 1043, 1108, 1175, 1244, 1315, 1388, 1463, 1540, 1619, 1700, 1783, 1868, 1955, 2044, 2135, 2228, 2323 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: (19 - 37*x + 20*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(19)*Pi*coth(sqrt(19)*Pi))/38. Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(19)*Pi*cosech(sqrt(19)*Pi))/38. (End) MAPLE A241849:=n->n^2+19: seq(A241849(n), n=0..100); # Wesley Ivan Hurt, Jan 16 2017 MATHEMATICA Table[n^2 + 19, {n, 0, 60}] LinearRecurrence[{3, -3, 1}, {19, 20, 23}, 50] (* Harvey P. Dale, Dec 05 2018 *) PROG (Magma) [n^2+19: n in [0..60]]; (PARI) a(n)=n^2+19 \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. similar sequences listed in A114962. Sequence in context: A007640 A265201 A274340 * A054304 A151979 A022109 Adjacent sequences: A241846 A241847 A241848 * A241850 A241851 A241852 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, May 01 2014 STATUS approved

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Last modified March 2 09:28 EST 2024. Contains 370461 sequences. (Running on oeis4.)