A051588 Number of 3 X n binary matrices such that any 2 rows have a common 1.

0, 1, 15, 175, 1827, 17791, 164955, 1475335, 12844707, 109581871, 920591595, 7643833495, 62904774387, 514168732351, 4180996130235, 33864296127655, 273465115692867, 2203291473841231, 17721094011796875, 142344054436901815

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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.

Index entries for linear recurrences with constant coefficients, signature (23,-194,712,-960).

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

Adjacent sequences: A051585 A051586 A051587 * A051589 A051590 A051591

Keyword

nonn,easy

Author

Vladeta Jovovic, Goran Kilibarda

Status

approved