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%I #26 Jul 04 2019 12:00:34
%S 4,1,12,37,76,129,196,277,372,481,604,741,892,1057,1236,1429,1636,
%T 1857,2092,2341,2604,2881,3172,3477,3796,4129,4476,4837,5212,5601,
%U 6004,6421,6852,7297,7756,8229,8716,9217,9732,10261,10804,11361,11932
%N a(n) = 7*n^2 + 4*n + 1.
%H G. C. Greubel, <a href="/A135704/b135704.txt">Table of n, a(n) for n = -1..1000</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 <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(-1)=4. - _Vincenzo Librandi_, Nov 18 2010
%F From _G. C. Greubel_, Oct 29 2016: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F G.f.: (4 - 11*x + 21*x^2)/(x * (1 - x)^3).
%F E.g.f.: 4/x + (1 + 11*x + 7*x^2)*exp(x). (End)
%t Table[7n^2+4n+1,{n,-1,50}] (* _Harvey P. Dale_, Mar 26 2011 *)
%t LinearRecurrence[{3,-3,1}, {4,1,12}, 25] (* _G. C. Greubel_, Oct 29 2016 *)
%o (PARI) a(n)=7*n^2+4*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y This is simply A005892 with offset -1.
%K nonn,easy
%O -1,1
%A _N. J. A. Sloane_, Mar 04 2008
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