A084485 Number of 3 X n 0-1 matrices which have n+2 1's and have no zero rows or zero columns.
1, 12, 90, 522, 2595, 11673, 49014, 195828, 753813, 2819475, 10308144, 36998118, 130786695, 456452493, 1575799290, 5389290792, 18281487081, 61569776727, 206040460212, 685584843450, 2269566343611, 7478425876977, 24538396875870, 80206515476892, 261239771497725
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
- Index entries for linear recurrences with constant coefficients, signature (15,-93,305,-558,540,-216)
Programs
-
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, 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 A := Matrix([L[i], L[j], L[k]]); if num1s(A, 3, n)=n+2 and (not has(Matrix([1, 1, 1]).A, 0)) then S := S+1; end if; od; od; od; S; end proc: seq (a(n), n=1..5);
-
Mathematica
a[n_] := n*(4*(3*n - 1)*3^n - 9*(n - 1)*2^n)/24; Array[a, 25] (* Jean-François Alcover, Nov 10 2017, after Vladeta Jovovic *)
Formula
a(n) = n*(4*(3*n-1)*3^n-9*(n-1)*2^n)/24. - Vladeta Jovovic, May 28 2003
G.f.: x*(1-3*x+3*x^2-17*x^3+33*x^4)/((3*x-1)^3*(2*x-1)^3). - Alois P. Heinz, Sep 24 2012
Extensions
Comment corrected by W. Edwin Clark, Sep 24 2012
Comments