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A006222 11*n^2 + 11*n + 3.
(Formerly M3109)
1

%I M3109 #32 Sep 08 2022 08:44:34

%S 3,25,69,135,223,333,465,619,795,993,1213,1455,1719,2005,2313,2643,

%T 2995,3369,3765,4183,4623,5085,5569,6075,6603,7153,7725,8319,8935,

%U 9573,10233,10915,11619,12345,13093,13863,14655,15469,16305

%N 11*n^2 + 11*n + 3.

%D G. V. Chudnovsky, Transcendental numbers, pp. 45-69 of Number Theory Carbondale 1979, Lect. Notes Math. 751 (1982).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A006222/b006222.txt">Table of n, a(n) for n = 0..1000</a>

%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 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.:(3+16*x+3*x^2)/(1-x)^3. - _Vincenzo Librandi_, Jul 07 2012

%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - _Vincenzo Librandi_, Jul 07 2012

%p A006222:=-(3+16*z+3*z**2)/(z-1)**3; [_Simon Plouffe_ in his 1992 dissertation.]

%t CoefficientList[Series[(3+16*x+3*x^2)/(1-x)^3,{x,0,50}],x] (* _Vincenzo Librandi_, Jul 07 2012 *)

%o (Magma) I:=[3, 25, 69]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Jul 07 2012

%o (PARI) a(n)=11*n^2+11*n+3 \\ _Charles R Greathouse IV_, Jun 17 2017

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_.

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)