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28-gonal pyramidal numbers: a(n) = n*(n+1)*(26*n-23)/6.
2

%I #35 Sep 08 2022 08:46:11

%S 0,1,29,110,270,535,931,1484,2220,3165,4345,5786,7514,9555,11935,

%T 14680,17816,21369,25365,29830,34790,40271,46299,52900,60100,67925,

%U 76401,85554,95410,105995,117335,129456,142384,156145,170765,186270,202686,220039,238355

%N 28-gonal pyramidal numbers: a(n) = n*(n+1)*(26*n-23)/6.

%C See comments in A256645.

%C This sequence is related to A051867 by a(n) = n*A051867(n) - Sum_{i=0..n-1} A051867(i). [_Bruno Berselli_, Apr 09 2015]

%D E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (26th row of the table).

%H Luciano Ancora, <a href="/A256648/b256648.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 + 25*x)/(1 - x)^4.

%F a(n) = A000292(n) + 25*A000292(n-1).

%t Table[n (n + 1)(26 n - 23)/6, {n, 0, 40}]

%t LinearRecurrence[{4, -6, 4, -1}, {0, 1, 29, 110}, 40] (* _Vincenzo Librandi_, Apr 08 2015 *)

%o (Magma) [n*(n+1)*(26*n-23)/6: n in [0..50]]; // _Vincenzo Librandi_, Apr 08 2015

%Y Partial sums of A161935.

%Y Cf. similar sequences listed in A237616.

%Y Cf. A000292, A051867.

%K nonn,easy

%O 0,3

%A _Luciano Ancora_, Apr 07 2015