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 A005892 Truncated square numbers: 7*n^2 + 4*n + 1. (Formerly M4833) 3
 1, 12, 37, 76, 129, 196, 277, 372, 481, 604, 741, 892, 1057, 1236, 1429, 1636, 1857, 2092, 2341, 2604, 2881, 3172, 3477, 3796, 4129, 4476, 4837, 5212, 5601, 6004, 6421, 6852, 7297, 7756, 8229, 8716, 9217, 9732, 10261, 10804, 11361, 11932 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 L. Hogben, Choice and Chance by Cardpack and Chessboard, Vol. 1, Max Parrish and Co, London, 1950, p. 36. Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = a(n-1) + 14*n - 3 (with a(0)=1). - Vincenzo Librandi, Nov 18 2010 From G. C. Greubel, Nov 30 2017: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). G.f.: (1 + 9*x + 4*x^2)/(1 - x)^3. E.g.f.: (1 + 11*x + 7*x^2)*exp(x). (End) MAPLE A005892:=-(1+9*z+4*z**2)/(z-1)**3; # Simon Plouffe in his 1992 dissertation MATHEMATICA Table[7n^2+4n+1, {n, 0, 50}] (* Harvey P. Dale, Mar 24 2011 *) PROG (PARI) a(n)=7*n^2+4*n+1 \\ Charles R Greathouse IV, Jun 17 2017 (Magma) [7*n^2 + 4*n + 1: n in [0..50]]; // G. C. Greubel, Nov 30 2017 (Sage) [7*n^2+4*n+1 for n in (0..50)] # G. C. Greubel, Apr 19 2019 CROSSREFS Cf. A135704. Sequence in context: A045174 A044089 A044470 * A266398 A041276 A302884 Adjacent sequences: A005889 A005890 A005891 * A005893 A005894 A005895 KEYWORD nonn,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from Frank Ellermann, Jan 18 2002 STATUS approved

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Last modified September 17 18:03 EDT 2024. Contains 375990 sequences. (Running on oeis4.)