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%I #24 Sep 08 2022 08:44:59
%S 0,1,15,175,1827,17791,164955,1475335,12844707,109581871,920591595,
%T 7643833495,62904774387,514168732351,4180996130235,33864296127655,
%U 273465115692867,2203291473841231,17721094011796875,142344054436901815
%N Number of 3 X n binary matrices such that any 2 rows have a common 1.
%H G. C. Greubel, <a href="/A051588/b051588.txt">Table of n, a(n) for n = 0..1000</a>
%H 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 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.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (23,-194,712,-960).
%F a(n) = 8^n - 3*6^n + 3*5^n - 4^n.
%F a(0)=0, a(1)=1, a(2)=15, a(3)=175, a(n) = 23*a(n-1) -194*a(n-2) + 712*a(n-3) -960*a(n-4). - _Harvey P. Dale_, Mar 07 2012
%F G.f.: x*(24*x^2-8*x+1)/((4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - _Colin Barker_, Nov 05 2012
%F E.g.f.: exp(8*x) -3*exp(6*x) +3*exp(5*x) -exp(4*x). - _G. C. Greubel_, Nov 12 2019
%p A051588:=n->8^n-3*6^n+3*5^n-4^n: seq(A051588(n), n=0..30); # _Wesley Ivan Hurt_, May 03 2017
%t Table[8^n-3*6^n+3*5^n-4^n, {n,0,20}] (* or *) LinearRecurrence[{23,-194, 712,-960}, {0,1,15,175}, 20] (* _Harvey P. Dale_, Mar 07 2012 *)
%o (PARI) vector(21, n, m=n-1; 8^m -3*6^m +3*5^m -4^m) \\ _G. C. Greubel_, Oct 06 2017
%o (Magma) [8^n -3*6^n +3*5^n -4^n: n in [0..20]]; // _G. C. Greubel_, Nov 12 2019
%o (Sage) [8^n -3*6^n +3*5^n -4^n for n in (0..20)] # _G. C. Greubel_, Nov 12 2019
%o (GAP) List([0..20], n-> 8^n -3*6^n +3*5^n -4^n); # _G. C. Greubel_, Nov 12 2019
%Y Cf. A005061.
%K nonn,easy
%O 0,3
%A _Vladeta Jovovic_, Goran Kilibarda
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