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 A027688 a(n) = n^2 + n + 3. 17
 3, 5, 9, 15, 23, 33, 45, 59, 75, 93, 113, 135, 159, 185, 213, 243, 275, 309, 345, 383, 423, 465, 509, 555, 603, 653, 705, 759, 815, 873, 933, 995, 1059, 1125, 1193, 1263, 1335, 1409, 1485, 1563, 1643, 1725, 1809, 1895, 1983, 2073, 2165, 2259 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Patrick De Geest, Palindromic Quasi_Over_Squares of the form n^2+(n+X). Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA For n>0: a(n) = A176271(n+1,2). - Reinhard Zumkeller, Apr 13 2010 a(n) = 2*n + a(n-1) (with a(0)=3). - Vincenzo Librandi, Aug 05 2010 From Colin Barker, Dec 29 2014: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). G.f.: (3*x^2 - 4*x + 3)/(1 - x)^3. (End) Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(11)/2)/sqrt(11). - Amiram Eldar, Jan 17 2021 MAPLE with (combinat):seq(fibonacci(3, n)+n+2, n=0..47); # Zerinvary Lajos, Jun 07 2008 MATHEMATICA Table[n^2 + n + 3, {n, 0, 50}] (* Bruno Berselli, Sep 03 2018 *) PROG (PARI) Vec((3*x^2-4*x+3)/(1-x)^3 + O(x^100)) \\ Colin Barker, Dec 29 2014 CROSSREFS Cf. A002522. Sequence in context: A095039 A022940 A025207 * A118403 A033498 A147493 Adjacent sequences:  A027685 A027686 A027687 * A027689 A027690 A027691 KEYWORD nonn,easy AUTHOR EXTENSIONS Definition and offset corrected by Franklin T. Adams-Watters, Jul 06 2009 STATUS approved

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Last modified April 10 19:06 EDT 2021. Contains 342853 sequences. (Running on oeis4.)