# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a125586 Showing 1-1 of 1 %I A125586 #16 May 06 2024 12:37:44 %S A125586 1,4,17,74,323,1400,6005,25478,107015,445556,1841273,7561922,30897227, %T A125586 125714672,509767421,2061390206,8317305359,33498803948,134727010049, %U A125586 541232563130,2172291241811,8712410196584,34922863258757,139921580805494,560408087592983 %N A125586 a(n) = 2^(2n-1) - (n+2)*3^(n-2). %C A125586 Number of n X n nonsingular real matrices with entries {0,1} in which the top left n-1 X n-1 submatrix is the identity matrix. See A125587 for proof. %C A125586 The number of singular matrices is given by A006234. %H A125586 Index entries for linear recurrences with constant coefficients, signature (10,-33,36). %F A125586 G.f.: -x*(10*x^2-6*x+1) / ((3*x-1)^2*(4*x-1)). - _Colin Barker_, Feb 26 2014 %e A125586 a(2) = 4: %e A125586 10 10 11 11 %e A125586 01 11 01 10 %p A125586 A125586:=n->2^(2n-1)-(n+2)*3^(n-2); seq(A125586(n), n=1..30); # _Wesley Ivan Hurt_, Feb 26 2014 %t A125586 Table[2^(2n-1)-(n+2)*3^(n-2), {n, 30}] (* _Wesley Ivan Hurt_, Feb 26 2014 *) %t A125586 LinearRecurrence[{10,-33,36},{1,4,17},50] (* _Harvey P. Dale_, Sep 15 2019 *) %o A125586 (PARI) Vec(-x*(10*x^2-6*x+1)/((3*x-1)^2*(4*x-1)) + O(x^100)) \\ _Colin Barker_, Feb 26 2014 %Y A125586 Cf. A125587, A006234. %K A125586 nonn,easy %O A125586 1,2 %A A125586 _N. J. A. Sloane_ and _Vinay Vaishampayan_, Jan 05 2007 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE