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%I #24 Feb 05 2024 09:26:51
%S 1,48,142,283,471,706,988,1317,1693,2116,2586,3103,3667,4278,4936,
%T 5641,6393,7192,8038,8931,9871,10858,11892,12973,14101,15276,16498,
%U 17767,19083,20446,21856,23313,24817,26368,27966,29611,31303,33042,34828,36661,38541
%N Centered 47-gonal numbers.
%H Vincenzo Librandi, <a href="/A129428/b129428.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = (1/2)*(2 + 47*n + 47*n^2).
%F From _Colin Barker_, Jul 27 2013: (Start)
%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
%F G.f.: (1 + 45*x + x^2)/(1-x)^3. (End)
%F E.g.f.: (1/2)*(2 + 94*x + 47*x^2)*exp(x). - _G. C. Greubel_, Feb 05 2024
%t LinearRecurrence[{3, -3, 1}, {1, 48, 142}, 70] (* _Vincenzo Librandi_, Sep 09 2016 *)
%o (Magma) [1+(47/2)*n+(47/2)*n^2: n in [0..50]]; // _Vincenzo Librandi_, Sep 09 2016
%o (PARI) a(n)=47*n*(n+1)/2+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%o (SageMath) [1+47*binomial(n+1,2) for n in range(51)] # _G. C. Greubel_, Feb 05 2024
%Y Cf. A095311, A130566, A130859, A130876.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Oct 06 2007, based on a suggestion from an unknown correspondent in 2004.
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