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A052387 Number of 3 X n binary matrices such that any 2 rows have a common 1, up to column permutations.

%I A052387 #24 Sep 08 2022 08:44:59
%S A052387 0,1,8,37,127,358,876,1926,3894,7359,13156,22451,36829,58396,89896,
%T A052387 134844,197676,283917,400368,555313,758747,1022626,1361140,1791010,
%U A052387 2331810,3006315,3840876,4865823,6115897,7630712,9455248
%N A052387 Number of 3 X n binary matrices such that any 2 rows have a common 1, up to column permutations.
%H A052387 G. C. Greubel, <a href="/A052387/b052387.txt">Table of n, a(n) for n = 0..1000</a>
%H A052387 V. Jovovic, G. Kilibarda, <a href="http://www.mathnet.ru/php/archive.phtml?wshow=paper&amp;jrnid=dm&amp;paperid=398&amp;option_lang=eng">On the number of Boolean functions in the Post classes F^{mu}_8</a>, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).
%H A052387 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A052387 a(n) = n*(n+1)*(n+2)*(n+3)*(n^3 +22*n^2 +53*n +134)/5040.
%F A052387 G.f.: -x*(x^3-x^2-1)/(x-1)^8. - _Colin Barker_, Nov 05 2012
%p A052387 A052387:=n->n*(n+1)*(n+2)*(n+3)*(n^3+22*n^2+53*n+134)/5040; seq(A052387(n), n=0..30); # _Wesley Ivan Hurt_, May 15 2014
%t A052387 Table[n*(n + 1)*(n + 2)*(n + 3)*(n^3 + 22*n^2 + 53*n + 134)/5040, {n,
%t A052387 0, 30}] (* _Wesley Ivan Hurt_, May 15 2014 *)
%o A052387 (Magma) [n*(n+1)*(n+2)*(n+3)*(n^3+22*n^2+53*n+134)/5040: n in [0..30]]; // _Wesley Ivan Hurt_, May 15 2014
%o A052387 (PARI) x='x+O('x^50); concat([0], Vec(-x*(x^3-x^2-1)/(x-1)^8)) \\ _G. C. Greubel_, Oct 07 2017
%Y A052387 Cf. A051588, A051587, A051589.
%K A052387 nonn,easy
%O A052387 0,3
%A A052387 _Vladeta Jovovic_, Goran Kilibarda, Mar 11 2000