A052388 Number of 4 X n binary matrices such that any 2 rows have a common 1, up to column permutations.

0, 1, 16, 146, 955, 4905, 20907, 76851, 250530, 739612, 2009177, 5085119, 12109526, 27348478, 58955082, 121956402, 243172488, 469115187, 878387366, 1600751976, 2845918041, 4946262815, 8419256605, 14057377245, 23055913530, 37192403430, 59075703351, 92488040301

Offset: 0

Author

Vladeta Jovovic, Goran Kilibarda, Mar 11 2000

Keywords

• nonn
• easy

References

• V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Crossrefs

Cf. A051588, A051587, A051589.

Programs

Magma

[n*(n+1)*(n+2)*(n+3)*(n+4)*(n^10 +110*n^9 +5445*n^8 +160050*n^7 +2906463*n^6 [phone]*n^5 [phone]*n^4 [phone]*n^3 [phone]*n^2 [phone]*n [phone])/1307674368000: n in [0..25]]; // G. C. Greubel, Oct 07 2017

Mathematica

CoefficientList[Series[-x*(x^10 -5*x^9 +10*x^8 -14*x^7 +21*x^6 -19*x^5 -5*x^4 +21*x^3 -10*x^2 -1)/(x-1)^16, {x, 0, 50}], x] (* G. C. Greubel, Oct 07 2017 *)

PARI

x='x+O('x^50); concat([0], Vec(-x*(x^10 -5*x^9 +10*x^8 -14*x^7 +21*x^6 -19*x^5 -5*x^4 +21*x^3 -10*x^2 -1)/(x-1)^16)) \\ G. C. Greubel, Oct 07 2017

Formula

a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n^10 +110*n^9 +5445*n^8 +160050*n^7 +2906463*n^6 [phone]*n^5 [phone]*n^4 [phone]*n^3 [phone]*n^2 [phone]*n [phone])/1307674368000.

G.f.: -x*(x^10 -5*x^9 +10*x^8 -14*x^7 +21*x^6 -19*x^5 -5*x^4 +21*x^3 -10*x^2 -1)/(x-1)^16. - Colin Barker, Nov 05 2012