0,3

We may assume n <= m since T(m,n)=T(n,m).

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T(1, 1) = 0; T(m, 1) = 1, m >= 2; T(m, 2) = m^2 + 2, m >= 2; T(m, 3) = 2*m^2 + 3 - m + 2*[m/2], m >= 3 D(m) = T(m, m) on the main diagonal: 0, 6, 20, 46, ...

When both m,n -> +oo, T(m,n) / 2Cmn -> 9/(2*pi^2). - Dan Dima (dimad72(AT)yahoo.com), Mar 18 2006

T(m,n) = m + n + 2*f(m,n) - 2*f([m/2],[n/2]) where: f(m,n) = (m-1)*(m - 1/2*m)*(n-1)*(n - 1/2*n) - [(m-1)/2]*(m - 2/2*[(m+1)/2])*[(n-1)/2]*(n - 2/2*[(n+1)/2]) - [(m-1)/3]*(m - 3/2*[(m+2)/3])*[(n-1)/3]*(n - 3/2*[(n+2)/3]) - [(m-1)/5]*(m - 5/2*[(m+4)/5])*[(n-1)/5]*(n - 5/2*[(n+4)/5]) - ... + [(m-1)/6]*(m - 6/2*[(m+5)/6])*[(n-1)/6]*(n - 6/2*[(n+5)/6]) + [(m-1)/10]*(m - 10/2*[(m+9)/10])*[(n-1)/10]*(n - 10/2*[(n+9)/10]) + ... - [(m-1)/30]*(m - 30/2*[(m+29)/30])*[(n-1)/30]*(n - 30/2*[(n+29)/30]) - ... + ... - ... - Dan Dima (dimad72(AT)yahoo.com), Mar 18 2006

Sequence in context: A082744 A127142 A046618 this_sequence A040041 A162933 A090850

Adjacent sequences: A107345 A107346 A107347 this_sequence A107349 A107350 A107351

nonn

Dan Dima (dimad72(AT)yahoo.com), May 23 2005