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%I #31 Feb 06 2023 06:16:27
%S 0,1,29,84,166,275,411,574,764,981,1225,1496,1794,2119,2471,2850,3256,
%T 3689,4149,4636,5150,5691,6259,6854,7476,8125,8801,9504,10234,10991,
%U 11775,12586,13424,14289,15181,16100,17046,18019,19019,20046,21100
%N 29-gonal numbers: a(n) = n*(27*n-25)/2.
%C See comments in A255184.
%D E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6 (27th row of the table).
%H Luciano Ancora, <a href="/A255187/b255187.txt">Table of n, a(n) for n = 0..1000</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 - 26*x)/(-1 + x)^3.
%F a(n) = A000217(n) + 26*A000217(n-1).
%F Product_{n>=2} (1 - 1/a(n)) = 27/29. - _Amiram Eldar_, Jan 22 2021
%F E.g.f.: exp(x)*(x + 27*x^2/2). - _Nikolaos Pantelidis_, Feb 06 2023
%t Table[n (27 n - 25)/2, {n, 40}]
%t PolygonalNumber[29,Range[0,40]] (* _Harvey P. Dale_, Jul 25 2021 *)
%o (PARI) a(n)=n*(27*n-25)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. similar sequences listed in A255184.
%K nonn,easy
%O 0,3
%A _Luciano Ancora_, Apr 04 2015
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