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A051588
Number of 3 X n binary matrices such that any 2 rows have a common 1.
7
0, 1, 15, 175, 1827, 17791, 164955, 1475335, 12844707, 109581871, 920591595, 7643833495, 62904774387, 514168732351, 4180996130235, 33864296127655, 273465115692867, 2203291473841231, 17721094011796875, 142344054436901815
OFFSET
0,3
LINKS
V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, (in Russian), Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.
FORMULA
a(n) = 8^n - 3*6^n + 3*5^n - 4^n.
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
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
E.g.f.: exp(8*x) -3*exp(6*x) +3*exp(5*x) -exp(4*x). - G. C. Greubel, Nov 12 2019
MAPLE
A051588:=n->8^n-3*6^n+3*5^n-4^n: seq(A051588(n), n=0..30); # Wesley Ivan Hurt, May 03 2017
MATHEMATICA
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 *)
PROG
(PARI) vector(21, n, m=n-1; 8^m -3*6^m +3*5^m -4^m) \\ G. C. Greubel, Oct 06 2017
(Magma) [8^n -3*6^n +3*5^n -4^n: n in [0..20]]; // G. C. Greubel, Nov 12 2019
(Sage) [8^n -3*6^n +3*5^n -4^n for n in (0..20)] # G. C. Greubel, Nov 12 2019
(GAP) List([0..20], n-> 8^n -3*6^n +3*5^n -4^n); # G. C. Greubel, Nov 12 2019
CROSSREFS
Cf. A005061.
Sequence in context: A107395 A036083 A346320 * A016164 A354135 A354137
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Goran Kilibarda
STATUS
approved