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 A294782 #15 Jan 31 2025 17:35:16
%S A294782 1,4,12,36,100,268,704,1812,4600,11556,28788,71252,175452,430284,
%T A294782 1051848,2564708,6240752,15161092,36784284,89155268,215911636,
%U A294782 522543436,1263991824,3056244212,7387384808,17851786148,43130479748,104187860340,251648811212,607755975820,1467673342616
%N A294782 Spherical growth of the Lamplighter group: number of elements in the Lamplighter group Z wr Z of length n with respect to the standard generating set {a,t}.
%C A294782 The group is presented by <a, t | 1 = [a, t^(-k) a t^k], for all k>.
%H A294782 Walter Parry, <a href="https://doi.org/10.1090/S0002-9947-1992-1062874-3">Growth series of some wreath products</a>, Trans. Amer. Math. Soc. 331 (1992), 751-759.
%H A294782 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4, -2, -4, -4, 4, 6, 4, 1).
%F A294782 G.f.: (1-x)^3 (1+x)^3 (1+x^2) / ((1-2x-x^2)(1-x-x^2-x^3)^2).
%e A294782 a(2)=12, since the elements of length 2 are a^2, at, at^-1, a^-2, a^-1t, a^-1t^-1, ta, ta^-1, t^2, t^-1a, t^-1a^-1, t^-2.
%t A294782 LinearRecurrence[{4,-2,-4,-4,4,6,4,1},{1,4,12,36,100,268,704,1812,4600},40] (* _Harvey P. Dale_, Jan 31 2025 *)
%Y A294782 Cf. A288348. First differences of A294781.
%K A294782 nonn
%O A294782 0,2
%A A294782 _Zoran Sunic_, Nov 08 2017