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A058482
Number of 3 X n binary matrices with no zero rows or columns.
3
1, 25, 265, 2161, 16081, 115465, 816985, 5745121, 40294561, 282298105, 1976795305, 13839692881, 96884227441, 678208723945, 4747518463225, 33232801429441, 232630126566721, 1628412435648985, 11398891698588745, 79792255837258801, 558545832702224401
OFFSET
1,2
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
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