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A056989 Number of nonsingular n X n (-1,0,1)-matrices (over the reals). 7
1, 2, 48, 11808, 27947520, 609653621760, 119288919620689920 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
It would be nice to have an estimate for the asymptotic rate of growth.
LINKS
Eric Weisstein's World of Mathematics, Nonsingular Matrix
FORMULA
a(n) = A060722(n) - A057981(n). - Alois P. Heinz, Dec 02 2019
EXAMPLE
a(1) = 2: [1], [ -1].
a(2) = 48: There are 8 choices for the first column, u (say) and then the 2nd column can be anything except 0, u, -u, so 6 choices, giving a total of 8*6 = 48.
MATHEMATICA
(* A brute force solution up to n = 4 *) a[n_] := a[n] = (m = Array[x, {n, n}]; cnt = 0; iter = {#, -1, 1}& /@ Flatten[m]; Do[ If[ Det[m] != 0, cnt++], Evaluate[ Sequence @@ iter]]; cnt); Table[ Print[a[n]]; a[n], {n, 1, 4}] (* Jean-François Alcover, Oct 11 2012 *)
CROSSREFS
Sequence in context: A002820 A196448 A053290 * A352207 A230886 A368132
KEYWORD
nonn,nice,more
AUTHOR
EXTENSIONS
a(4) from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 27 2000
Entry revised by N. J. A. Sloane, Jan 02 2007
a(5) from Giovanni Resta, Feb 20 2009
a(0)=1 prepended by Alois P. Heinz, Dec 02 2019
a(0)-a(5) confirmed and a(6) added by Minfeng Wang, May 01 2024
STATUS
approved

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Last modified July 21 02:16 EDT 2024. Contains 374462 sequences. (Running on oeis4.)