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%I M4833 #51 Sep 08 2022 08:44:34
%S 1,12,37,76,129,196,277,372,481,604,741,892,1057,1236,1429,1636,1857,
%T 2092,2341,2604,2881,3172,3477,3796,4129,4476,4837,5212,5601,6004,
%U 6421,6852,7297,7756,8229,8716,9217,9732,10261,10804,11361,11932
%N Truncated square numbers: 7*n^2 + 4*n + 1.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H G. C. Greubel, <a href="/A005892/b005892.txt">Table of n, a(n) for n = 0..5000</a>
%H L. Hogben, <a href="https://archive.org/details/chanceandchoiceb029729mbp/page/n39">Choice and Chance by Cardpack and Chessboard</a>, Vol. 1, Max Parrish and Co, London, 1950, p. 36.
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H B. K. Teo and N. J. A. Sloane, <a href="http://neilsloane.com/doc/magic1/magic1.html">Magic numbers in polygonal and polyhedral clusters</a>, Inorgan. Chem. 24 (1985), 4545-4558.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = a(n-1) + 14*n - 3 (with a(0)=1). - _Vincenzo Librandi_, Nov 18 2010
%F From _G. C. Greubel_, Nov 30 2017: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F G.f.: (1 + 9*x + 4*x^2)/(1 - x)^3.
%F E.g.f.: (1 + 11*x + 7*x^2)*exp(x). (End)
%p A005892:=-(1+9*z+4*z**2)/(z-1)**3; # _Simon Plouffe_ in his 1992 dissertation
%t Table[7n^2+4n+1,{n,0,50}] (* _Harvey P. Dale_, Mar 24 2011 *)
%o (PARI) a(n)=7*n^2+4*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%o (Magma) [7*n^2 + 4*n + 1: n in [0..50]]; // _G. C. Greubel_, Nov 30 2017
%o (Sage) [7*n^2+4*n+1 for n in (0..50)] # _G. C. Greubel_, Apr 19 2019
%Y Cf. A135704.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Frank Ellermann_, Jan 18 2002
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