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 A373322 #21 Jun 23 2024 21:26:28
%S A373322 1,1,1,3,3,9,9,29,29,99,99,351,351,1273,1273,4679,4679,17341,17341,
%T A373322 64637,64637,242019,242019,909789,909789,3432751,3432751,12998311,
%U A373322 12998311,49387289,49387289,188261329,188261329,719860679,719860679,2760525963,2760525963,10614508493,10614508493
%N A373322 The number of indecomposable summands, counted with multiplicity, in tensor powers of the vector representation of SL2 in characteristic 2.
%C A373322 In characteristic zero the analogous numbers are A001405.
%H A373322 K. Coulembier, P. Etingof, V. Ostrik, and D. Tubbenhauer, <a href="https://arxiv.org/abs/2405.16786">Fractal behavior of tensor powers of the two dimensional space in prime characteristic</a>, arXiv:2405.16786 [math.RT], 2024.
%H A373322 M. Larsen, <a href="https://arxiv.org/abs/2405.16015">Bounds for SL2-indecomposables in tensor powers of the natural representation in characteristic 2</a>, arXiv:2405.16015 [math.RT], 2024.
%H A373322 Daniel Tubbenhauer, <a href="https://github.com/dtubbenhauer/sl2-charp">GitHub page</a>
%F A373322 a(0) = a(1) = 1, and for n>1: a(2n-1) = a(2n) = Sum_{k=0..n-1} binomial(n-1,k)*2^(n-1-k)*a(k).
%F A373322 a(n) ~ h(n)*n^(t)*2^n for t=1/2log_2(3/2)-1 approx. -0.707 and h(n) a bounded function. The constant t is A153460 - 2.
%t A373322 a[0|1] = 1; a[n_] := a[n] = With[{m = Ceiling[n/2]}, Sum[Binomial[m-1, k] 2^(m-1-k) a[k], {k, 0, m-1}]]; Table[a[n], {n, 0, 40}]
%o A373322 (PARI) a(n) = if (n<=1, 1, my(m=ceil(n/2)); sum(k=0, m-1, binomial(m-1,k)*2^(m-1-k)*a(k))); \\ _Michel Marcus_, Jun 01 2024
%Y A373322 Cf. A001405 (for characteristic zero), A153460.
%K A373322 nonn
%O A373322 0,4
%A A373322 _Daniel Tubbenhauer_, Jun 01 2024