The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A071302

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A071302

a(n) = (1/2) * (number of n X n 0..2 matrices M with MM' mod 3 = I, where M' is the transpose of M and I is the n X n identity matrix).
(history; published version)

#56 by Michel Marcus at Mon Nov 07 02:28:06 EST 2022

STATUS

reviewed

approved

#55 by Joerg Arndt at Mon Nov 07 02:13:30 EST 2022

STATUS

proposed

reviewed

#54 by Jon E. Schoenfield at Mon Nov 07 00:24:36 EST 2022

STATUS

editing

proposed

#53 by Jon E. Schoenfield at Mon Nov 07 00:24:34 EST 2022

COMMENTS

Also, number of x n X n orthogonal matrices over GF(3) with determinant 1. - Max Alekseyev, Nov 06 2022

STATUS

proposed

editing

#52 by Jon E. Schoenfield at Sun Nov 06 22:20:00 EST 2022

STATUS

editing

proposed

#51 by Jon E. Schoenfield at Sun Nov 06 22:19:58 EST 2022

NAME

a(n) = (1/2 times the ) * (number of n X n 0..2 matrices M with MM' mod 3 = I, where M' is the transpose of M and I is the n X n identity matrix).

FORMULA

a(2k+1) = 3^k * Prod_Product_{i=0..k-1} (3^(2k) - 3^(2i)); a(2k) = (3^k + (-1)^(k+1)) * Prod_Product_{i=1..k-1} (3^(2k) - 3^(2i)) (see MacWilliams, 1969). - Max Alekseyev, Nov 06 2022

STATUS

proposed

editing

#50 by Max Alekseyev at Sun Nov 06 21:46:33 EST 2022

STATUS

editing

proposed

#49 by Max Alekseyev at Sun Nov 06 21:46:27 EST 2022

LINKS

Jessie MacWilliams, <a href="https://doi.org/10.2307/2317262">Orthogonal Matrices Over Finite Fields</a>, The American Mathematical Monthly 76:2 (1969), 152-164.

CROSSREFS

Cf. A003053, A003920, A060968, A071303, A071304, A071305, A071306, A071307, A071308, A071309, A071310, A071900, A087784, A208895, A264083, A318609.

STATUS

proposed

editing

#48 by Max Alekseyev at Sun Nov 06 20:46:21 EST 2022

STATUS

editing

proposed

#47 by Max Alekseyev at Sun Nov 06 20:46:01 EST 2022

COMMENTS

Even though the sequence has only 7 known terms (as of the time of this note), the conjecture below is based on the work (formulas, comments, etc.) by Jianing Song for sequence A318609. - Petros Hadjicostas, Dec 18 2019

FORMULA

Conjecture: a(n+1) = a(n) * A318609(n+1) for n >= 1. - _conjectured by _Petros Hadjicostas_, Dec 18 2019; proved based on the explicit formula by _Max Alekseyev_, Nov 06 2022