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.
%I A099930 #42 May 07 2025 09:40:39
%S A099930 1,12,174,2436,34307,482664,6791772,95567064,1344731653,18921807828,
%T A099930 266250046986,3746422451772,52716164405255,741772724044560,
%U A099930 10437534301224120,146867252940711408,2066579075472320521,29078974309550454492,409172219409185308518,5757490046038128779316
%N A099930 a(n) = Pell(n) * Pell(n-1) * Pell(n-2) / 10.
%H A099930 Michael A. Allen and Kenneth Edwards, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/60-5/allen.pdf">Fence tiling derived identities involving the metallonacci numbers squared or cubed</a>, Fib. Q. 60:5 (2022) 5-17.
%H A099930 N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, arXiv:math/0509316 [math.NT], 2005-2006.
%H A099930 N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://dx.doi.org/10.1016/j.jcta.2006.03.018">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%H A099930 Ronald Orozco López, <a href="https://arxiv.org/abs/2408.08943">Generating Functions of Generalized Simplicial Polytopic Numbers and (s,t)-Derivatives of Partial Theta Function</a>, arXiv:2408.08943 [math.CO], 2024. See p. 13.
%H A099930 Ronald Orozco López, <a href="https://arxiv.org/abs/2501.11490">Simplicial d-Polytopic Numbers Defined on Generalized Fibonacci Polynomials</a>, arXiv:2501.11490 [math.CO], 2025. See p. 10.
%H A099930 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,30,-12,-1).
%F A099930 G.f.: x^3 / ((1+2*x-x^2)*(1-14*x-x^2)).
%F A099930 a(n) = 12*a(n-1) + 30*a(n-2) - 12*a(n-3) - a(n-4); a(3)=1, a(4)=12, a(5)=174, a(6)=2436. - _Harvey P. Dale_, Feb 26 2012
%F A099930 From _Peter Bala_, Mar 30 2015: (Start)
%F A099930 The following remarks assume an offset of 0.
%F A099930 The o.g.f. A(x) = 1/( (1 + 2*x - x^2)*(1 - 14*x - x^2) ). Hence A(x) (mod 4) = 1/(1 + 2*x - x^2)^2 (mod 4). It follows by Theorem 1 of Heninger et al. that sqrt(A(x)) = 1 + 6*x + 69*x^2 + 804*x^3 + ... has integral coefficients.
%F A099930 Sum_{n >= 0} a(n+3)*x^n = exp( Sum_{n >= 1} Pell(4*n)/Pell(n)*x^n/n ). Cf. A001656, A084175. (End)
%F A099930 a(n+1) = (1/2)*Sum_{k=1..n-1} ( A014445(k)*A110272(n-k) ) for n > 1. - _Michael A. Allen_, Jan 25 2023
%t A099930 Drop[CoefficientList[Series[x^3/((1+2x-x^2)(1-14x-x^2)),{x,0,20}],x],3] (* or *) LinearRecurrence[{12,30,-12,-1},{1,12,174,2436},20] (* _Harvey P. Dale_, Feb 26 2012 *)
%Y A099930 Cf. A000129. Third column of triangle A099927. Cf. A001656, A084175.
%K A099930 nonn,easy
%O A099930 3,2
%A A099930 _Ralf Stephan_, Nov 03 2004