OFFSET
0,4
COMMENTS
I.e. T(n,k) = sum_{m in M(n,k)} checks(m), where M(n,k) contains all n by k matrices and checks(M) is the number of checks to find all nonzero rows and columns of m.
REFERENCES
M.R.C. van Dongen, Technical Report: TR0004, CS Dept, UCC, College Road, Cork, Ireland
FORMULA
T(0, k) = 0, T(n, 0) = 0, T(n, k) = 2^(n k)( n(2 - 2^(1-k)) + (1-k)2^(1-n) + 2 Sum^k_{c=2} (1-2^(-c))^(n))
EXAMPLE
{0}; {0,0}; {0,2,0}; {0,8,8,0}; {0,24,58,24,0}; ...
MATHEMATICA
T[0, k_] := 0 T[n_, 0] := 0 T[n_, k_] := 2^(n k)( n(2 - 2^(1-k)) + (1-k)2^(1-n) + 2 Sum(1-2^(-c))^(n), {c, 2, k}]) For[c=0, c<=10, c++, For[n=0, n<=c, n++, Print[T[n, c-n]]]]
CROSSREFS
KEYWORD
AUTHOR
M.R.C. van Dongen (dongen(AT)cs.ucc.ie), Dec 24 2000
STATUS
approved