_Paul Barry (pbarry(AT)wit.ie), _, Jul 21 2003

Alternatively, triangle read by rows with formula t(n,m)=If[n == 0 || n == m || m == 0, 1, n - m]*If[n == m || n == 0 || m == 0, 1, m]. - _Roger L. Bagula (rlbagulatftn(AT)yahoo.com), _, Sep 06 2008

t[n_, m_] = If[ n == 0 || n == m || m == 0, 1, n - m]*If[n == m || n == 0 || m == 0, 1, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] - _Roger L. Bagula (rlbagulatftn(AT)yahoo.com), _, Sep 06 2008

Alternatively, triangle read by rows with formula t(n,m)=If[n == 0 || n == m || m == 0, 1, n - m]*If[n == m || n == 0 || m == 0, 1, m]. - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 06 2008

As a triangle:

{1},

{1, 1},

{1, 1, 1},

{1, 2, 2, 1},

{1, 3, 4, 3, 1},

{1, 4, 6, 6, 4, 1},

{1, 5, 8, 9, 8, 5, 1},

{1, 6, 10, 12, 12, 10, 6, 1},

{1, 7, 12, 15, 16, 15, 12, 7, 1},

{1, 8, 14, 18, 20, 20, 18, 14, 8, 1},

{1, 9, 16, 21, 24, 25, 24, 21, 16, 9, 1}

t[n_, m_] = If[ n == 0 || n == m || m == 0, 1, n - m]*If[n == m || n == 0 || m == 0, 1, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 06 2008

easy,nonn,tabl,new

T(0, k)=T(n, 0)=1, T(n, k)=nk+0^n, n, k>0

easy,nonn,tabl,new

Rows include A028310, A004277, A008486, A008574, A008706, A008458. Main diagonal is n^2+0^n (A000290, preceded by extra 1).

easy,nonn,tabl,new

Symmetric version of square array A086460.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 4, 3, 1, 1, 4, 6, 6, 4, 1, 1, 5, 8, 9, 8, 5, 1, 1, 6, 10, 12, 12, 10, 6, 1, 1, 7, 12, 15, 16, 15, 12, 7, 1, 1, 8, 14, 18, 20, 20, 18, 14, 8, 1, 1, 9, 16, 21, 24, 25, 24, 21, 16, 9, 1, 1, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 1, 1, 11, 20, 27, 32, 35, 36

0,8

Rows include A028310,A004277,A008486,A008574,A008706,A008458. Main diagonal is n^2+0^n (A000290, preceded by extra 1).

T(0,k)=T(n,0)=1, T(n,k)=nk+0^n, n,k>0

Rows begin

1 1 1 1 1 ...

1 1 2 3 4 ...

1 2 4 6 8 ...

1 3 6 9 12 ...

1 4 8 12 16 ...

easy,nonn,tabl

Paul Barry (pbarry(AT)wit.ie), Jul 21 2003

approved