A051587 Number of 4 X n binary matrices such that any 2 rows have a common 1.

0, 1, 31, 781, 17887, 380821, 7635991, 145858861, 2680379887, 47772681541, 831224886151, 14192847754141, 238791235611487, 3971678627940661, 65470546978625911, 1071778956904132621, 17451563620410100687

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..825

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 (73,-2287,40195,-433744,2944132,-12279888,28782720,-29030400).

Formula

a(n) = 16^n -6*12^n +12*10^n -9^n -16*8^n +15*7^n -6*6^n +5^n.

G.f.: x*(167040*x^6-146736*x^5+48916*x^4-8424*x^3+805*x^2-42*x+1)/((5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)*(9*x-1)*(10*x-1)*(12*x-1)*(16*x-1)). - Colin Barker, Nov 05 2012

E.g.f.: exp(16*x) -6*exp(12*x) +12*exp(10*x) -exp(9*x) -16*exp(8*x) +15*exp(7*x) -6*exp(6*x) +exp(5*x). - G. C. Greubel, Nov 12 2019

Maple

seq(16^n -6*12^n +12*10^n -9^n -16*8^n +15*7^n -6*6^n +5^n, n=0..20); # G. C. Greubel, Nov 12 2019

Mathematica

Table[16^n -6*12^n +12*10^n -9^n -16*8^n +15*7^n -6*6^n +5^n, {n, 0, 20}] (* G. C. Greubel, Oct 06 2017 *)

Prog

(PARI) vector(21, n, m=n-1; 16^m -6*12^m +12*10^m -9^m -16*8^m +15*7^m -6*6^m +5^m) \\ G. C. Greubel, Oct 06 2017
(Magma) [16^n -6*12^n +12*10^n -9^n -16*8^n +15*7^n -6*6^n +5^n: n in [0..20]]; // G. C. Greubel, Oct 06 2017
(Sage) [16^n -6*12^n +12*10^n -9^n -16*8^n +15*7^n -6*6^n +5^n for n in (0..20)] # G. C. Greubel, Nov 12 2019
(GAP) List([0..20], n-> 16^n -6*12^n +12*10^n -9^n -16*8^n +15*7^n -6*6^n +5^n); # G. C. Greubel, Nov 12 2019

Crossrefs

Sequence in context: A061252 A096049 A166488 * A069380 A006111 A183828

Adjacent sequences: A051584 A051585 A051586 * A051588 A051589 A051590

Keyword

nonn,easy

Author

Vladeta Jovovic, Goran Kilibarda

Status

approved