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A014799 Squares of odd pentagonal pyramidal numbers.

%I A014799 #35 Feb 16 2025 08:32:33
%S A014799 1,5625,164025,1399489,6765201,23532201,66015625,159138225,342731169,
%T A014799 676572121,1246160601,2169230625,3603000625,5752160649,8877596841,
%U A014799 13305853201,19439330625,27767223225,38877191929,53467775361
%N A014799 Squares of odd pentagonal pyramidal numbers.
%H A014799 Vincenzo Librandi, <a href="/A014799/b014799.txt">Table of n, a(n) for n = 0..1000</a>
%H A014799 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalPyramidalNumber.html">Pentagonal Pyramidal Number</a>
%F A014799 From _Colin Barker_, Apr 17 2012: (Start)
%F A014799 a(n) = (1 + 2*n)^2*(1 + 4*n)^4.
%F A014799 G.f.: (1 + 5618*x + 124671*x^2 + 369404*x^3 + 216463*x^4 + 21042*x^5 + 81*x^6) /(1-x)^7. (End)
%F A014799 a(n) = A015223(n)^2. - _R. J. Mathar_, Jul 30 2016
%p A014799 seq( (1+2*n)^2*(1+4*n)^4, n=0..30); # _Muniru A Asiru_, Oct 09 2017
%t A014799 Table[(1+2*n)^2*(1+4*n)^4,{n,0,20}] (* _Vincenzo Librandi_, Apr 18 2012 *)
%t A014799 Range[0,20]//(1+2*#)^2*(1+4*#)^4& (* _Waldemar Puszkarz_, Oct 11 2017 *)
%o A014799 (Magma) [(1+2*n)^2*(1+4*n)^4: n in [0..30]]; // _Vincenzo Librandi_, Apr 18 2012
%o A014799 (GAP) A014799:=List(Filtered(List([0..10^2], n->n^2*(n+1)/2),IsOddInt),i->i^2); # _Muniru A Asiru_, Oct 09 2017
%Y A014799 Cf. A002411, A014800, A015223, A015224.
%K A014799 nonn,easy
%O A014799 0,2
%A A014799 _Mohammad K. Azarian_