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.

A063249 Doubly hexagonal numbers.

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%I A063249 #17 Jun 17 2017 03:06:04
%S A063249 0,1,66,435,1540,4005,8646,16471,28680,46665,72010,106491,152076,
%T A063249 210925,285390,378015,491536,628881,793170,987715,1216020,1481781,
%U A063249 1788886,2141415,2543640,3000025,3515226,4094091,4741660,5463165
%N A063249 Doubly hexagonal numbers.
%H A063249 William A. Tedeschi, <a href="/A063249/b063249.txt">Table of n, a(n) for n = 0..10000</a>
%H A063249 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A063249 a(n) = n*(2*n-1)(4*n^2-2*n-1) = A000384(A000384(n)).
%F A063249 G.f.: -x*(15*x^3+115*x^2+61*x+1) / (x-1)^5. - _Colin Barker_, Sep 14 2014
%e A063249 a(2)=66 since 6 is the 2nd hexagonal number and 66 is the 6th hexagonal number.
%t A063249 LinearRecurrence[{5,-10,10,-5,1},{0,1,66,435,1540},30] (* _Harvey P. Dale_, Dec 02 2016 *)
%o A063249 (PARI) concat(0, Vec(-x*(15*x^3+115*x^2+61*x+1)/(x-1)^5 + O(x^100))) \\ _Colin Barker_, Sep 14 2014
%Y A063249 Cf. A002817 for doubly triangular numbers, A000583 for doubly square numbers and A232713 for doubly pentagonal numbers.
%K A063249 nonn,easy
%O A063249 0,3
%A A063249 _Henry Bottomley_, Jul 11 2001