OFFSET
0,5
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_{c=2..k} (1-2^(-c))^n).
EXAMPLE
Triangle begins:
{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}]);
Table[T[n, c-n], {c, 0, 10}, {n, 0, c}]//Flatten
CROSSREFS
KEYWORD
AUTHOR
M.R.C. van Dongen (dongen(AT)cs.ucc.ie), Dec 24 2000
EXTENSIONS
a(0) = 0 added by Jason Yuen, Jun 01 2025
STATUS
approved
