A058482 Number of 3 X n binary matrices with no zero rows or columns.

1, 25, 265, 2161, 16081, 115465, 816985, 5745121, 40294561, 282298105, 1976795305, 13839692881, 96884227441, 678208723945, 4747518463225, 33232801429441, 232630126566721, 1628412435648985, 11398891698588745, 79792255837258801, 558545832702224401

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Index entries for linear recurrences with constant coefficients, signature (11,-31,21).

Formula

Number of m X n binary matrices with no zero rows or columns is Sum_{j=0..m}(-1)^j*C(m, j)*(2^(m-j)-1)^n.

a(n) = 7^n-3*3^n+3.

a(n) = 11*a(n-1)-31*a(n-2)+21*a(n-3). G.f.: -x*(21*x^2+14*x+1) / ((x-1)*(3*x-1)*(7*x-1)). - Colin Barker, Jul 10 2013

Mathematica

LinearRecurrence[{11, -31, 21}, {1, 25, 265}, 30] (* Harvey P. Dale, Aug 15 2014 *)

Prog

(PARI) a(n) = 7^n-3*3^n+3 \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Cf. A055602, A024206, A055609 (unlabeled case), A058481, column 3 of A183109 and A218695.

Sequence in context: A164756 A221781 A298717 * A114932 A329537 A012859

Adjacent sequences: A058479 A058480 A058481 * A058483 A058484 A058485

Keyword

easy,nonn,nice

Author

Vladeta Jovovic, Nov 26 2000

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Dec 04 2000

More terms from Colin Barker, Jul 10 2013

Status

approved