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%I #45 Sep 08 2022 08:46:11
%S 0,1,27,102,250,495,861,1372,2052,2925,4015,5346,6942,8827,11025,
%T 13560,16456,19737,23427,27550,32130,37191,42757,48852,55500,62725,
%U 70551,79002,88102,97875,108345,119536,131472,144177,157675,171990,187146,203167,220077
%N 26-gonal pyramidal numbers: a(n) = n*(n+1)*(8*n-7)/2.
%C See comments in A256645.
%D E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (24th row of the table).
%H Luciano Ancora, <a href="/A256646/b256646.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 + 23*x)/(1 - x)^4.
%F a(n) = A000292(n) + 23*A000292(n-1).
%F a(n) = n*A051866(n) - Sum_{i=0..n-1} A051866(i). - _Bruno Berselli_, Apr 09 2015
%F Sum_{n>=1} 1/a(n) = 2*(4*(sqrt(2)+1)*Pi - 4*(sqrt(2)-8)*log(2) + 8*sqrt(2)*log(sqrt(2)+2) - 7)/105. - _Amiram Eldar_, Jan 10 2022
%t Table[n (n + 1) (8 n - 7)/2, {n, 0, 40}]
%t LinearRecurrence[{4, -6, 4, -1}, {0, 1, 27, 102}, 40] (* _Vincenzo Librandi_, Apr 08 2015 *)
%o (Magma) [n*(n+1)*(8*n-7)/2: n in [0..50]]; // _Vincenzo Librandi_, Apr 08 2015
%Y Partial sums of A255185.
%Y Cf. similar sequences listed in A237616.
%Y Cf. A000292, A051866.
%K nonn,easy
%O 0,3
%A _Luciano Ancora_, Apr 07 2015
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