This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%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 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, 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