A125586 a(n) = 2^(2n-1) - (n+2)*3^(n-2).

1, 4, 17, 74, 323, 1400, 6005, 25478, 107015, 445556, 1841273, 7561922, 30897227, 125714672, 509767421, 2061390206, 8317305359, 33498803948, 134727010049, 541232563130, 2172291241811, 8712410196584, 34922863258757, 139921580805494, 560408087592983

Offset: 1

Author

N. J. A. Sloane and Vinay Vaishampayan, Jan 05 2007

Keywords

• nonn
• easy

Comments

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.

The number of singular matrices is given by A006234.

Examples

			a(2) = 4:
10 10 11 11
01 11 01 10
		

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-33,36).

Crossrefs

Cf. A125587, A006234.

Programs

Maple

A125586:=n->2^(2n-1)-(n+2)*3^(n-2); seq(A125586(n), n=1..30); # Wesley Ivan Hurt, Feb 26 2014

Mathematica

Table[2^(2n-1)-(n+2)*3^(n-2), {n, 30}] (* Wesley Ivan Hurt, Feb 26 2014 *)
LinearRecurrence[{10,-33,36},{1,4,17},50] (* Harvey P. Dale, Sep 15 2019 *)

PARI

Vec(-x*(10*x^2-6*x+1)/((3*x-1)^2*(4*x-1)) + O(x^100)) \\ Colin Barker, Feb 26 2014

Formula

G.f.: -x*(10*x^2-6*x+1) / ((3*x-1)^2*(4*x-1)). - Colin Barker, Feb 26 2014