cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A014801 Squares of odd hexagonal pyramidal numbers.

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%I A014801 #29 May 25 2025 16:45:25
%S A014801 1,49,9025,25921,275625,511225,2393209,3705625,11675889,16378209,
%T A014801 40844881,53831569,115025625,145226601,278055625,340218025,600103009,
%U A014801 716900625,1186595809,1391066209,2188461961,2526771289,3813680025
%N A014801 Squares of odd hexagonal pyramidal numbers.
%H A014801 Vincenzo Librandi, <a href="/A014801/b014801.txt">Table of n, a(n) for n = 0..1000</a>
%H A014801 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).
%F A014801 G.f.: -(9*x^12 +160*x^11 +15402*x^10 +24624*x^9 +244415*x^8 +151296*x^7 +518380*x^6 +134944*x^5 +195863*x^4 +16608*x^3 +8970*x^2 +48*x +1)/((x -1)^7*(x +1)^6). [_Colin Barker_, Nov 16 2012]
%F A014801 a(n) = A015225(n)^2. - _R. J. Mathar_, Jul 30 2016
%F A014801 a(n) == 1 (mod 8). - _Hugo Pfoertner_, Feb 07 2024
%t A014801 CoefficientList[Series[- (9 x^12 + 160 x^11 + 15402 x^10 + 24624 x^9 + 244415 x^8 + 151296 x^7 + 518380 x^6 + 134944 x^5 + 195863 x^4 + 16608 x^3 + 8970 x^2 + 48 x + 1)/((x - 1)^7 (x + 1)^6), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)
%t A014801 LinearRecurrence[{1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1},{1,49,9025,25921,275625,511225,2393209,3705625,11675889,16378209,40844881,53831569,115025625},30] (* _Harvey P. Dale_, May 25 2025 *)
%K A014801 nonn,easy
%O A014801 0,2
%A A014801 _Mohammad K. Azarian_