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 A001545 a(n) = (5n+1)*(5n+4). 2
 4, 54, 154, 304, 504, 754, 1054, 1404, 1804, 2254, 2754, 3304, 3904, 4554, 5254, 6004, 6804, 7654, 8554, 9504, 10504, 11554, 12654, 13804, 15004, 16254, 17554, 18904, 20304, 21754, 23254, 24804, 26404, 28054, 29754, 31504, 33304, 35154, 37054, 39004, 41004 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA Equals 50 * A000217(n) + 4. a(n) = 50*n + a(n-1) with a(0)=4. - Vincenzo Librandi, Jan 20 2011 From Amiram Eldar, Jan 23 2022: (Start) Sum_{n>=0} 1/a(n) = sqrt(1 + 2/sqrt(5))*Pi/15 = 0.2882687.... Sum_{n>=0} (-1)^n/a(n) = 2*log(phi)/(3*sqrt(5)) + 2*log(2)/15, where phi is the golden ratio (A001622). Product_{n>=0} (1 - 1/a(n)) = sqrt(2 + 2/sqrt(5)) * cos(sqrt(13)*Pi/10). Product_{n>=0} (1 + 1/a(n)) = sqrt(2 + 2/sqrt(5)) * cos(Pi/(2*sqrt(5))). Product_{n>=0} (1 + 2/a(n)) = phi. (End) G.f.: -2*(2+21*x+2*x^2)/(x-1)^3 . - R. J. Mathar, May 30 2022 Sum_{n>=0) 1/a(n) = (Psi(4/5) -Psi(1/5))/15. See A200135, A200138. - R. J. Mathar, May 30 2022 MATHEMATICA Table[(5n+1)(5n+4), {n, 0, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {4, 54, 154}, 60] (* Harvey P. Dale, Mar 17 2019 *) PROG (PARI) a(n)=(5*n+1)*(5*n+4) \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A000217, A001622, A177059. Sequence in context: A362050 A095210 A156469 * A208954 A269507 A302942 Adjacent sequences: A001542 A001543 A001544 * A001546 A001547 A001548 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified December 2 22:48 EST 2023. Contains 367526 sequences. (Running on oeis4.)