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30-gonal numbers: a(n) = n*(14*n-13).
15

%I #35 Feb 06 2023 06:06:33

%S 0,1,30,87,172,285,426,595,792,1017,1270,1551,1860,2197,2562,2955,

%T 3376,3825,4302,4807,5340,5901,6490,7107,7752,8425,9126,9855,10612,

%U 11397,12210,13051,13920,14817,15742,16695,17676,18685,19722,20787,21880

%N 30-gonal numbers: a(n) = n*(14*n-13).

%C See comments in A255184.

%C Also star 15-gonal numbers.

%D E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6 (28th row of the table).

%H Luciano Ancora, <a href="/A254474/b254474.txt">Table of n, a(n) for n = 0..1000</a>

%H Luciano Ancora, <a href="/A256645/a256645_1.pdf">Polygonal and Pyramidal numbers</a>, Section 1.

%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 - 27*x)/(-1 + x)^3.

%F a(n) = A000217(n) + 27*A000217(n-1).

%F a(n) = A051867(n) + 15*A000217(n-1).

%F Product_{n>=2} (1 - 1/a(n)) = 14/15. - _Amiram Eldar_, Jan 22 2021

%F E.g.f.: exp(x)*(x + 14*x^2). - _Nikolaos Pantelidis_, Feb 05 2023

%t Table[n (14 n - 13), {n, 40}]

%o (PARI) a(n)=n*(14*n-13) \\ _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