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1, 7, 25, 79, 241, 727, 2185, 6559, 19681, 59047, 177145, 531439, 1594321, 4782967, 14348905, 43046719, 129140161, 387420487, 1162261465, 3486784399, 10460353201, 31381059607, 94143178825, 282429536479, 847288609441
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 2 X n binary matrices with no zero rows or columns.
a(n)^2+2*a(n+1)+1 is a square number, i. e. a(n)^2+2*a(n+1)+1=[a(n)+3]^2: for n=2, a(2)^2+2*a(3)+1=7^2+2*25+1=100=(7+3)^2; for n=3, a(3)^2+2*a(4)+1=25^2+2*79+1=784=(25+3)^2. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Apr 23 2010]
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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.
G.f.: 1/(1-3*x)-2/(1-x). E.g.f.: e^(3*x)-2*(e^x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), Jan 14 2009]
a(n)=3*a(n-1)+4 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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EXAMPLE
| For n=2, a(2)=3*1+4=7; n=3, a(3)=3*7+4=25; n=4, a(4)=3*25+4=79 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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MATHEMATICA
| a=1; lst={a}; Do[a=a*3+4; AppendTo[lst, a], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 25 2008]
3^Range[30]-2 (* From Harvey P. Dale, Mar 28 2011 *)
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CROSSREFS
| Cf. A055602, A024206 (unlabeled case), A055609, A058482, A000244.
Cf. A003462, A007051, A034472, A024023, A067771, A029858, A134931, A115099, A100774, A079004 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 25 2008]
Sequence in context: A155254 A155295 A168589 * A155294 A155233 A183914
Adjacent sequences: A058478 A058479 A058480 * A058482 A058483 A058484
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 26 2000
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Dec 04 2000
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