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%I #32 Sep 08 2022 08:46:11
%S 0,1,31,118,290,575,1001,1596,2388,3405,4675,6226,8086,10283,12845,
%T 15800,19176,23001,27303,32110,37450,43351,49841,56948,64700,73125,
%U 82251,92106,102718,114115,126325,139376,153296,168113,183855,200550,218226,236911,256633
%N 30-gonal pyramidal numbers: a(n) = n*(n+1)*(28*n-25)/6.
%C See comments in A256645.
%C This sequence is related to A051868 by a(n) = n*A051868(n) - Sum_{i=0..n-1} A051868(i). [_Bruno Berselli_, Apr 09 2015]
%D E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (28th row of the table).
%H Luciano Ancora, <a href="/A256650/b256650.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 + 27*x)/(1 - x)^4.
%F a(n) = A000292(n) + 27*A000292(n-1).
%t Table[n (n + 1) (28 n - 25)/6, {n, 0, 40}]
%t LinearRecurrence[{4, -6, 4, -1}, {0, 1, 31, 118}, 40] (* _Vincenzo Librandi_, Apr 08 2015 *)
%o (Magma) [n*(n+1)*(28*n-25)/6: n in [0..50]]; // _Vincenzo Librandi_, Apr 08 2015
%Y Partial sums of A254474.
%Y Cf. similar sequences listed in A237616.
%Y Cf. A000292, A051868.
%K nonn,easy
%O 0,3
%A _Luciano Ancora_, Apr 07 2015
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