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27-gonal numbers: a(n) = n*(25*n-23)/2.
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%I #28 Feb 06 2023 06:06:17

%S 0,1,27,78,154,255,381,532,708,909,1135,1386,1662,1963,2289,2640,3016,

%T 3417,3843,4294,4770,5271,5797,6348,6924,7525,8151,8802,9478,10179,

%U 10905,11656,12432,13233,14059,14910,15786,16687,17613,18564,19540

%N 27-gonal numbers: a(n) = n*(25*n-23)/2.

%C See comments in A255184.

%D E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6 (25th row of the table).

%H Luciano Ancora, <a href="/A255186/b255186.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 - 24*x)/(-1 + x)^3.

%F a(n) = A000217(n) + 24*A000217(n-1).

%F Product_{n>=2} (1 - 1/a(n)) = 25/27. - _Amiram Eldar_, Jan 22 2021

%F E.g.f.: exp(x)*(x + 25*x^2/2). - _Nikolaos Pantelidis_, Feb 06 2023

%t Table[n (25 n - 23)/2, {n, 40}]

%o (PARI) a(n)=n*(25*n-23)/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