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 A003956 #56 Jul 07 2025 03:32:01
%S A003956 8,192,92160,743178240,97029351014400,203286581427673497600,
%T A003956 6819500449352277792129024000,3660967964237442812098963052691456000,
%U A003956 31446995505814020383166371418359014222725120000
%N A003956 Order of complex Clifford group of degree 2^n arising in quantum coding theory.
%H A003956 T. D. Noe, <a href="/A003956/b003956.txt">Table of n, a(n) for n = 0..20</a>
%H A003956 Simon Burton, Elijah Durso-Sabina, and Natalie C. Brown, <a href="https://arxiv.org/abs/2406.09951">Genons, Double Covers and Fault-tolerant Clifford Gates</a>, arXiv:2406.09951 [quant-ph], 2024. See p. 18.
%H A003956 A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, <a href="https://arxiv.org/abs/quant-ph/9608006">Quantum error correction via codes over GF(4)</a>, arXiv:quant-ph/9608006, 1996-1997; IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.
%H A003956 G. Nebe, E. M. Rains, and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0001038">The invariants of the Clifford groups</a>, arXiv:math/0001038 [math.CO], 2000; Des. Codes Crypt. 24 (2001), 99-121.
%H A003956 G. Nebe, E. M. Rains, and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.
%H A003956 Edwin Pednault, <a href="https://arxiv.org/abs/2303.08287">An alternative approach to optimal wire cutting without ancilla qubits</a>, arXiv:2303.08287 [quant-ph], 2023.
%H A003956 Tefjol Pllaha, Olav Tirkkonen, and Robert Calderbank, <a href="https://arxiv.org/abs/2102.12384">Binary Subspace Chirps</a>, arXiv:2102.12384 [cs.IT], 2021.
%H A003956 Bernhard Runge, <a href="https://doi.org/10.1016/0012-365X(94)00271-J">Codes and Siegel modular forms</a>, Discrete Math. 148 (1996), 175-204.
%H A003956 Peter Selinger, <a href="https://arxiv.org/abs/1310.6813">Generators and relations for n-qubit Clifford operators</a>, arXiv:1310.6813 [quant-ph], 2013; Log. Methods Comput. Sci. 11 (2:10) (2015), 1-17, doi:10.2168/LMCS-11(2:10)2015.
%H A003956 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>.
%F A003956 From _Amiram Eldar_, Jul 06 2025: (Start)
%F A003956 a(n) = 2^(n^2+2*n+3) * Product_{k=1..n} (4^k-1).
%F A003956 a(n) ~ c * 2^(2*n^2+3*n+3), where c = A100221. (End)
%p A003956 a(n):= 2^(n^2+2*n+3)*mul(4^j-1, j=1..n); seq(a(n), n=0..10); # modified by _G. C. Greubel_, Sep 24 2019
%t A003956 Table[2^(n^2+2n+3) Product[4^j-1,{j,n}],{n,0,10}] (* _Harvey P. Dale_, Nov 03 2017 *)
%o A003956 (PARI) vector(11, n, 2^(n^2 +2)*prod(j=1,n-1, 4^j-1) ) \\ _G. C. Greubel_, Sep 24 2019
%o A003956 (Magma) [n eq 0 select 8 else 2^((n+1)^2+2)*(&*[4^j-1: j in [1..n]]): n in [0..10]]; // _G. C. Greubel_, Sep 24 2019
%o A003956 (Sage) [2^((n+1)^2 +2)*product(4^j -1 for j in (1..n)) for n in (0..10)] # _G. C. Greubel_, Sep 24 2019
%o A003956 (GAP) List([0..10], n-> 2^((n+1)^2 +2)*Product([1..n], j-> 4^j -1) ); # _G. C. Greubel_, Sep 24 2019
%o A003956 (Python)
%o A003956 from math import prod
%o A003956 def A003956(n): return prod((1<<i)-1 for i in range(2,2*n+1,2)) << n*(n+2)+3 # _Chai Wah Wu_, Jun 20 2022
%Y A003956 Cf. A001309, A014116, A014115, A027672, A100221.
%Y A003956 Equals twice A027638.
%K A003956 nonn,easy,nice
%O A003956 0,1
%A A003956 _N. J. A. Sloane_ and _Peter Shor_