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

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A005061.

Programs

GAP

List([0..20], n-> 8^n -3*6^n +3*5^n -4^n); # G. C. Greubel, Nov 12 2019

Magma

[8^n -3*6^n +3*5^n -4^n: n in [0..20]]; // 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 *)

PARI

vector(21, n, m=n-1; 8^m -3*6^m +3*5^m -4^m) \\ G. C. Greubel, Oct 06 2017

Sage

[8^n -3*6^n +3*5^n -4^n for n in (0..20)] # G. C. Greubel, Nov 12 2019

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