A084486 Number of 4 X n 0-1 matrices which have n+3 1's and have no zero rows or zero columns.
1, 32, 522, 5776, 50600, 380424, 2570932, 16073600, 94748400, 533515240, 2896652396, 15268777440, 78544641448, 395875164104, 1960998472260, 9570684204544, 46112171619296, 219682468794600, 1036237335593500
Offset: 1
Links
- M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550, 2013. - From N. J. A. Sloane, Feb 13 2013
- M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5
Programs
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Maple
with(LinearAlgebra): num1s := (M,m,n)->add(ListTools[Flatten](convert(M,listlist))[j],j=1..m*n): binrows := n->[seq(convert(i+2^n,base,2)[1..n],i=1..2^n-1)]; a := proc(n) local A,L,i,j,k,el,S,M: S := 0: L := binrows(n): for i from 1 to 2^n-1 do for j from 1 to 2^n-1 do for k from 1 to 2^n-1 do for el from 1 to 2^n-1 do A := Matrix([L[i],L[j],L[k],L[el]]); if num1s(A,4,n)=n+3 and (not has(Matrix([1,1,1,1]).A,0)) then S := S+1; end if; od; od; od; od; S; end proc: seq (a(n), n=1..2);
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Mathematica
a[n_] := n/48*((27*4^n - 32*3^n + 6*2^n)*n^2 + (-9*4^n + 32*3^n - 18*2^n)*n + (-6*4^n + 12*2^n)); Array[a, 20] (* Jean-François Alcover, Nov 10 2017, after Vladeta Jovovic *)
Formula
n/48*((27*4^n-32*3^n+6*2^n)*n^2+(-9*4^n+32*3^n-18*2^n)*n+(-6*4^n+12*2^n)). - Vladeta Jovovic, May 28 2003
G.f.: x * (1 -4*x -40*x^2 +44*x^3 +2885*x^4 -19624*x^5 +59014*x^6 -97728*x^7 +98064*x^8 -67200*x^9 +28800*x^10) / ((3*x-1)^4*(2*x-1)^4*(4*x-1)^4). - Alois P. Heinz, Sep 24 2012
Extensions
Comment corrected by W. Edwin Clark, Sep 24 2012
Comments