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27-gonal pyramidal numbers: a(n) = n*(n+1)*(25*n-22)/6.
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%I #35 Sep 08 2022 08:46:11

%S 0,1,28,106,260,515,896,1428,2136,3045,4180,5566,7228,9191,11480,

%T 14120,17136,20553,24396,28690,33460,38731,44528,50876,57800,65325,

%U 73476,82278,91756,101935,112840,124496,136928,150161,164220,179130,194916,211603,229216

%N 27-gonal pyramidal numbers: a(n) = n*(n+1)*(25*n-22)/6.

%C See comments in A256645.

%D E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (25th row of the table).

%H Luciano Ancora, <a href="/A256647/b256647.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 3.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F G.f.: x*(1 + 24*x)/(1 - x)^4.

%F a(n) = A000292(n) + 24*A000292(n-1).

%t Table[n (n + 1) (25 n - 22)/6, {n, 0, 40}]

%t LinearRecurrence[{4, -6, 4, -1}, {0, 1, 28, 106}, 40] (* _Vincenzo Librandi_, Apr 08 2015 *)

%o (Magma) [n*(n+1)*(25*n-22)/6: n in [0..50]]; // _Vincenzo Librandi_, Apr 08 2015

%Y Partial sums of A255186.

%Y Cf. similar sequences listed in A237616.

%Y Cf. A000292.

%K nonn,easy

%O 0,3

%A _Luciano Ancora_, Apr 07 2015