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%I A051589 #19 Sep 08 2022 08:44:59
%S A051589 0,1,63,3367,167835,7803391,339133803,13887495007,541044196875,
%T A051589 20237096702431,732455240043243,25820836854042847,891331324715015115,
%U A051589 30260208833985800671,1013882831306569043883,33620617443978687281887,1105857774681062127612555
%N A051589 Number of 5xn binary matrices such that any 2 rows have a common 1.
%H A051589 Vincenzo Librandi, <a href="/A051589/b051589.txt">Table of n, a(n) for n = 0..670</a>
%H A051589 V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.4213/dm398">On the number of Boolean functions in the Post classes F^{mu}_8</a>, (in Russian), Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
%H A051589 V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.1515/dma.1999.9.6.593">On the number of Boolean functions in the Post classes F^{mu}_8</a>, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.
%F A051589 a(n) = 32^n - 10*24^n + 30*20^n - 5*18^n + 5*17^n - 70*16^n - 30*15^n + 135*14^n + 30*13^n - 140*12^n - 2*11^n + 130*10^n - 110*9^n + 45*8^n - 10*7^n + 6^n.
%F A051589 G.f.: x*(933561925632000*x^14 -1286309121638400*x^13 +786606914672640*x^12 -287219252934144*x^11 +70324589076096*x^10 -12248067009984*x^9 +1568017231256*x^8 -150181430252*x^7 +10834851518*x^6 -587198697*x^5 +23594853*x^4 -684354*x^3 +13636*x^2 -169*x +1) / ((6*x -1)*(7*x -1)*(8*x -1)*(9*x -1)*(10*x -1)*(11*x -1)*(12*x -1)*(13*x -1)*(14*x -1)*(15*x -1)*(16*x -1)*(17*x -1)*(18*x -1)*(20*x -1)*(24*x -1)*(32*x -1)). - _Colin Barker_, Feb 22 2013
%p A051589 A051589(n):=32^n -10*24^n +30*20^n -5*18^n +5*17^n -70*16^n -30*15^n + 135*14^n +30*13^n -140*12^n -2*11^n +130*10^n -110*9^n +45*8^n -10*7^n +6^n; seq(A051589(n), n=0..20); # _G. C. Greubel_, Nov 12 2019
%t A051589 Table[32^n -10*24^n +30*20^n -5*18^n +5*17^n -70*16^n -30*15^n +135*14^n +30*13^n -140*12^n -2*11^n +130*10^n -110*9^n +45*8^n -10*7^n +6^n, {n, 0, 30}] (* _Vincenzo Librandi_, Sep 18 2018 *)
%o A051589 (Magma) [32^n-10*24^n+30*20^n-5*18^n+5*17^n-70*16^n-30*15^n +135*14^n +30*13^n-140*12^n-2*11^n+130*10^n-110*9^n+45*8^n-10*7^n +6^n: n in [0..20]]; // _Vincenzo Librandi_, Sep 18 2018
%o A051589 (PARI) vector(21, n, m=n-1; 32^m -10*24^m +30*20^m -5*18^m +5*17^m -70*16^m -30*15^m +135*14^m +30*13^m -140*12^m -2*11^m +130*10^m -110*9^m +45*8^m -10*7^m +6^m) \\ _G. C. Greubel_, Nov 12 2019
%o A051589 (Sage) [32^n-10*24^n+30*20^n-5*18^n+5*17^n-70*16^n-30*15^n +135*14^n +30*13^n-140*12^n-2*11^n+130*10^n-110*9^n+45*8^n-10*7^n +6^n for n in (0..20)] # _G. C. Greubel_, Nov 12 2019
%o A051589 (GAP) List([0..20], n-> 32^n-10*24^n+30*20^n-5*18^n+5*17^n-70*16^n-30*15^n +135*14^n +30*13^n-140*12^n-2*11^n+130*10^n-110*9^n+45*8^n-10*7^n +6^n); # _G. C. Greubel_, Nov 12 2019
%Y A051589 Cf. A005061, A051587, A051588.
%K A051589 nonn
%O A051589 0,3
%A A051589 _Vladeta Jovovic_, Goran Kilibarda. Revised Aug 03 2000.

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