OFFSET
0,3
COMMENTS
Also number of linear orthomorphisms of GF(2)^n.
REFERENCES
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).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..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.
FORMULA
Reference gives a recurrence.
a(n) = 2^(n(n-1)/2) * A005327(n+1).
MAPLE
# (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=0..15)];
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Mar 17 2000
Entry revised by N. J. A. Sloane, Aug 10 2011
a(0)=1 prepended by Alois P. Heinz, Jan 10 2025
STATUS
approved