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 A017330 a(n) = (10*n + 5)^2. 5
 25, 225, 625, 1225, 2025, 3025, 4225, 5625, 7225, 9025, 11025, 13225, 15625, 18225, 21025, 24025, 27225, 30625, 34225, 38025, 42025, 46225, 50625, 55225, 60025, 65025, 70225, 75625, 81225, 87025, 93025, 99225, 105625, 112225, 119025, 126025, 133225, 140625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This is an old school trick which says that a square of an integer that ends with 5 is easy to compute. Remove the 5, multiply the remaining number by (itself + 1), and concatenate 25 at the end. So, a(n)\100 = A002378(n). - Michel Marcus, Dec 23 2013 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: -25*(x^2 + 6*x + 1)/(x - 1)^3. - Colin Barker, Nov 14 2012 a(n) = A017329(n)^2. - Michel Marcus, Dec 23 2013 a(0) = 25, a(n) = a(n - 1) + 200*n. - Alonso del Arte, Feb 25 2020 From Amiram Eldar, Apr 18 2023: (Start) a(n) = 5^2 * A016754(n). Sum_{n>=0} 1/a(n) = Pi^2/200. Sum_{n>=0} (-1)^n/a(n) = G/25, where G is Catalan's constant (A006752). (End) EXAMPLE 5^2 = 25; 15^2 = (1 * 2) concatenate 25 = 225; 25^2 = (2 * 3) concatenate 25 = 625; 35^2 = (3 * 4) concatenate 25 = 1225; 45^2 = (4 * 5) concatenate 25 = 2025; 55^2 = (5 * 6) concatenate 25 = 3025; 65^2 = (6 * 7) concatenate 25 = 4225, etc. MATHEMATICA 25Range[1, 89, 2]^2 (* Alonso del Arte, Feb 25 2020 *) PROG (Magma) [(10*n+5)^2: n in [0..35]]; // Vincenzo Librandi, Aug 02 2011 (PARI) a(n)=(10*n+5)^2 \\ Charles R Greathouse IV, Jun 17 2017 (Scala) (5 to 445 by 10).map(n => n * n) // Alonso del Arte, Feb 25 2020 CROSSREFS Cf. A002378, A006752, A016754. Sequence in context: A030484 A225135 A038692 * A135509 A295015 A288876 Adjacent sequences: A017327 A017328 A017329 * A017331 A017332 A017333 KEYWORD nonn,easy AUTHOR N. J. A. Sloane. EXTENSIONS More terms from Michel Marcus, Dec 23 2013 STATUS approved

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Last modified February 21 08:45 EST 2024. Contains 370228 sequences. (Running on oeis4.)