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 A056989 Number of nonsingular n X n (-1,0,1)-matrices (over the reals). 6
 1, 2, 48, 11808, 27947520, 609653621760 (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]. 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 Cf. A055165, A053290, A056990, A055165, A002884, A046747, A057981, A060722. Sequence in context: A002820 A196448 A053290 * A230886 A090770 A081960 Adjacent sequences:  A056986 A056987 A056988 * A056990 A056991 A056992 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 STATUS approved

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Last modified May 26 13:49 EDT 2020. Contains 334626 sequences. (Running on oeis4.)