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%I #14 Sep 08 2022 08:45:30
%S 1,48,186,460,915,1596,2548,3816,5445,7480,9966,12948,16471,20580,
%T 25320,30736,36873,43776,51490,60060,69531,79948,91356,103800,117325,
%U 131976,147798,164836,183135,202740,223696,246048,269841,295120,321930,350316,380323
%N Pyramidal 47-gonal numbers.
%H Vincenzo Librandi, <a href="/A130566/b130566.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F (15 n + 1) (n + 2) (n + 1)/2.
%F G.f.: (1+44*x)/(1-x)^4. [_Colin Barker_, Apr 30 2012]
%F a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - _Vincenzo Librandi_, Jun 29 2012
%t CoefficientList[Series[(1+44*x)/(1-x)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Jun 29 2012 *)
%o (Magma) I:=[1, 48, 186, 460]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Jun 29 2012
%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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