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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 Table of n, a(n) for n=0..6. Minfeng Wang, C++ program to calculate A056989 Eric Weisstein's World of Mathematics, Nonsingular Matrix Index entries for sequences related to binary matrices 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 Cf. A055165, A053290, A056990, A055165, A002884, A046747, A057981, A060722. Sequence in context: A002820 A196448 A053290 * A352207 A230886 A368132 Adjacent sequences: A056986 A056987 A056988 * A056990 A056991 A056992 KEYWORD nonn,nice,more AUTHOR Eric W. Weisstein 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.)