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 A027865 Sums of six consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2. 10
 55, 91, 139, 199, 271, 355, 451, 559, 679, 811, 955, 1111, 1279, 1459, 1651, 1855, 2071, 2299, 2539, 2791, 3055, 3331, 3619, 3919, 4231, 4555, 4891, 5239, 5599, 5971, 6355, 6751, 7159, 7579, 8011, 8455, 8911, 9379, 9859, 10351, 10855, 11371, 11899, 12439, 12991 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS From Jean-Christophe Hervé, Nov 11 2015: (Start) a(n) is defined for n < 0 and a(-n) = a(n-5) for any n; a(-4) = a(-1) = 31, a(-3) = a(-2) = 19. a(n) == 3 (mod 4) for all n in Z, hence a(n) is never square. (End) LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Patrick De Geest, World!Of Numbers. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 6*n^2 + 30*n + 55. G.f.: (55 - 74*x + 31*x^2) / (1-x)^3. - R. J. Mathar, Jun 11 2013 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 12*(n+2). - Jean-Christophe Hervé, Nov 11 2015 E.g.f.: (55 + 36*x + 6*x^2)*exp(x). - G. C. Greubel, Aug 25 2022 Sum_{n>=0} 1/a(n) = tanh(sqrt(35/3)*Pi/2)*Pi/(2*sqrt(105)) - 50/589. - Amiram Eldar, Sep 15 2022 MAPLE A027865:=n->6*n^2 + 30*n + 55: seq(A027865(n), n=0..60); # Wesley Ivan Hurt, Nov 12 2015 MATHEMATICA Table[Total@ Map[#^2 &, n + Range[0, 5]], {n, 0, 34}] (* Michael De Vlieger, Nov 12 2015 *) Total/@Partition[Range[0, 40]^2, 6, 1] (* or *) Table[6x^2+30x+55, {x, 0, 40}] (* Harvey P. Dale, Mar 23 2018 *) PROG (PARI) a(n)=6*n^2+30*n+55 \\ Charles R Greathouse IV, Jul 28 2015 (PARI) Vec((-31*x^2+74*x-55)/(x-1)^3 + O(x^50)) \\ Altug Alkan, Nov 12 2015 CROSSREFS Cf. A000290, A001844, A027575, A027578, A120328, A260637, A276026. Sequence in context: A039533 A157484 A230125 * A247681 A195118 A143205 Adjacent sequences: A027862 A027863 A027864 * A027866 A027867 A027868 KEYWORD nonn,easy AUTHOR EXTENSIONS Corrected by Ralf Stephan, Jan 02 2005 Edited by Charles R Greathouse IV, Jul 25 2010 Renamed by Jean-Christophe Hervé, Nov 12 2015 STATUS approved

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Last modified March 29 15:28 EDT 2023. Contains 361599 sequences. (Running on oeis4.)