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
Links
- Index entries for linear recurrences with constant coefficients, signature (11,-31,21).
Programs
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Mathematica
LinearRecurrence[{11,-31,21},{1,25,265},30] (* Harvey P. Dale, Aug 15 2014 *) -
PARI
a(n) = 7^n-3*3^n+3 \\ Charles R Greathouse IV, Feb 10 2017
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
Extensions
More terms from Larry Reeves (larryr(AT)acm.org), Dec 04 2000
More terms from Colin Barker, Jul 10 2013