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A003956 Order of complex Clifford group of degree 2^n arising in quantum coding theory. 14
8, 192, 92160, 743178240, 97029351014400, 203286581427673497600, 6819500449352277792129024000, 3660967964237442812098963052691456000, 31446995505814020383166371418359014222725120000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, Quantum error correction via codes over GF(4), arXiv:quant-ph/9608006, 1996-1997; IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.
G. Nebe, E. M. Rains and N. J. A. Sloane, The invariants of the Clifford groups, arXiv:math/0001038 [math.CO], 2000; Des. Codes Crypt. 24 (2001), 99-121.
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
Edwin Pednault, An alternative approach to optimal wire cutting without ancilla qubits, arXiv:2303.08287 [quant-ph], 2023.
Tefjol Pllaha, Olav Tirkkonen, and Robert Calderbank, Binary Subspace Chirps, arXiv:2102.12384 [cs.IT], 2021.
B. Runge, Codes and Siegel modular forms, Discrete Math. 148 (1996), 175-204.
MAPLE
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
MATHEMATICA
Table[2^(n^2+2n+3) Product[4^j-1, {j, n}], {n, 0, 10}] (* Harvey P. Dale, Nov 03 2017 *)
PROG
(PARI) vector(11, n, 2^(n^2 +2)*prod(j=1, n-1, 4^j-1) ) \\ G. C. Greubel, Sep 24 2019
(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
(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
(GAP) List([0..10], n-> 2^((n+1)^2 +2)*Product([1..n], j-> 4^j -1) ); # G. C. Greubel, Sep 24 2019
(Python)
from math import prod
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
CROSSREFS
Equals twice A027638.
Sequence in context: A071303 A128406 A265269 * A204820 A041269 A172340
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved

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Last modified April 21 14:03 EDT 2024. Contains 371870 sequences. (Running on oeis4.)