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75-gonal numbers: a(n) = n*(73*n-71)/2.
1

%I #34 Feb 10 2023 10:50:45

%S 0,1,75,222,442,735,1101,1540,2052,2637,3295,4026,4830,5707,6657,7680,

%T 8776,9945,11187,12502,13890,15351,16885,18492,20172,21925,23751,

%U 25650,27622,29667,31785,33976,36240,38577,40987,43470,46026,48655,51357,54132,56980,59901,62895,65962,69102,72315,75601,78960,82392,85897,89475

%N 75-gonal numbers: a(n) = n*(73*n-71)/2.

%H Daniel Starodubtsev, <a href="/A098230/b098230.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

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

%F G.f.: -x*(1+72*x) / (x-1)^3. - _R. J. Mathar_, Feb 05 2011

%F a(n) = n*(73*n - 71)/2.

%F E.g.f.: exp(x)*(x + 73*x^2/2). - _Nikolaos Pantelidis_, Feb 10 2023

%p A098230 := proc(n) n*(73*n-71)/2 ; end proc:

%p seq(A098230(n),n=0..20) ; # _R. J. Mathar_, Feb 04 2011

%o (Magma) [ n*(73*n - 71)/2: n in [0..50] ]; // _Vincenzo Librandi_, Feb 04 2011

%o (PARI) a(n)=n*(73*n-71)/2 \\ _Charles R Greathouse IV_, Oct 16 2015

%Y Cf. A051867, A051873.

%K nonn,easy

%O 0,3

%A _Parthasarathy Nambi_, Oct 25 2004