A052387 Number of 3 X n binary matrices such that any 2 rows have a common 1, up to column permutations.
0, 1, 8, 37, 127, 358, 876, 1926, 3894, 7359, 13156, 22451, 36829, 58396, 89896, 134844, 197676, 283917, 400368, 555313, 758747, 1022626, 1361140, 1791010, 2331810, 3006315, 3840876, 4865823, 6115897, 7630712, 9455248
Offset: 0
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, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).
- Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
Programs
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Magma
[n*(n+1)*(n+2)*(n+3)*(n^3+22*n^2+53*n+134)/5040: n in [0..30]]; // Wesley Ivan Hurt, May 15 2014
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Maple
A052387:=n->n*(n+1)*(n+2)*(n+3)*(n^3+22*n^2+53*n+134)/5040; seq(A052387(n), n=0..30); # Wesley Ivan Hurt, May 15 2014
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Mathematica
Table[n*(n + 1)*(n + 2)*(n + 3)*(n^3 + 22*n^2 + 53*n + 134)/5040, {n, 0, 30}] (* Wesley Ivan Hurt, May 15 2014 *) -
PARI
x='x+O('x^50); concat([0], Vec(-x*(x^3-x^2-1)/(x-1)^8)) \\ G. C. Greubel, Oct 07 2017
Formula
a(n) = n*(n+1)*(n+2)*(n+3)*(n^3 +22*n^2 +53*n +134)/5040.
G.f.: -x*(x^3-x^2-1)/(x-1)^8. - Colin Barker, Nov 05 2012