The OEIS is supported by the many generous donors to the OEIS Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002820 Number of n X n invertible binary matrices A such that A+I is invertible.
(Formerly M2170 N0866)
0, 2, 48, 5824, 2887680, 5821595648, 47317927329792, 1544457148312846336, 202039706313624586813440, 105823549214125066767168438272, 221819704567105547916502447159246848 (list; graph; refs; listen; history; text; internal format)



Also number of linear orthomorphisms of GF(2)^n.


N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Vincenzo Librandi, Table of n, a(n) for n = 1..55

Zong Duo Dai, Solomon W. Golomb, and Guang Gong, Generating all linear orthomorphisms without repetition, Discrete Math. 205 (1999), 47-55.

P. F. Duvall, Jr. and P. W. Harley, III, A note on counting matrices, SIAM J. Appl. Math., 20 (1971), 374-377.

Hsien-Kuei Hwang, Emma Yu Jin, and Michael J. Schlosser, Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow, arXiv:2012.13570 [math.CO], 2020.

Kent Morrison, Matrices over F_q with no eigenvalues of 0 or 1

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

Index entries for sequences related to binary matrices


Reference gives a recurrence.

a(n) = 2^(n(n-1)/2) * A005327(n+1).


(Maple program based on Dai et al. from N. J. A. Sloane, Aug 10 2011)

N:=proc(n, i) option remember; if i = 1 then 1 else (2^n-2^(i-1))*N(n, i-1); fi; end;

Oh:=proc(n) option remember; local r; global N;

if n=0 then RETURN(1) elif n=1 then RETURN(0) else

add( 2^(r-2)*N(n, r)*2^(r*(n-r))*Oh(n-r), r=2..n); fi; end;

[seq(Oh(n), n=1..15)];


ni[n_, i_] := ni[n, i] = If[i == 1, 1, (2^n - 2^(i-1))*ni[n, i-1]]; a[0] = 1; a[1] = 0; a[n_] := a[n] = Sum[ 2^(r-2)*ni[n, r]*2^(r*(n-r))*a[n-r], {r, 2, n}]; Table[a[n], {n, 1, 11}] (* Jean-François Alcover, Jan 19 2012, after Maple *)


Cf. A002884.

Sequence in context: A067626 A053071 A238838 * A196448 A053290 A056989

Adjacent sequences: A002817 A002818 A002819 * A002821 A002822 A002823




N. J. A. Sloane


More terms from Vladeta Jovovic, Mar 17 2000

Entry revised by N. J. A. Sloane, Aug 10 2011



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 14:43 EST 2022. Contains 358644 sequences. (Running on oeis4.)