A127069 Number of lines in a Pauli graph of order n.

15, 45, 153, 561, 2145, 8385, 33153, 131841, 525825, 2100225, 8394753, 33566721, 134242305, 536920065, 2147581953, 8590131201, 34360131585, 137439739905, 549757386753, 2199026401281, 8796099313665, 35184384671745

Offset

2,1

Comments

Apparently a duplicate of A028401. - Michel Marcus, May 28 2019

The number of vertices in a Pauli graph of order n is (4^n) - 1. Other invariants and a(n), are given in Table 5, p. 11, of Planat and Saniga.

Links

Table of n, a(n) for n=2..23.

Michel R. P. Planat and Metod Saniga, Pauli graph and finite projective lines/geometries, arXiv:quant-ph/0703154, 2007.

Formula

Conjectures from Colin Barker, May 28 2019: (Start)

G.f.: 3*x^2*(5 - 20*x + 16*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)).

a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n>4.

a(n) = (2 + 3*2^n + 4^n) / 2 for n>1.

(End)

Prog

(PARI) a(n) = my(t=2^(n-1), alfa=2^t-1, s=2*alfa); (t+1)*(s*t+alfa)/alfa; \\ Michel Marcus, May 28 2019

Crossrefs

Appears to be A028401.

Sequence in context: A072251 A002756 A039450 * A346853 A241731 A095129

Adjacent sequences: A127066 A127067 A127068 * A127070 A127071 A127072

Keyword

nonn

Author

Jonathan Vos Post, Mar 21 2007

Extensions

More terms from Michel Marcus, May 28 2019

Status

approved