A086461 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
Offset: 0
Examples
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 ...
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}
Programs
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Mathematica
t[n_, m_] = If[ n == 0 || n == m || m == 0, 1, n - m]*If[n == m || n == 0 || m == 0, 1, m]; Table[t[n, m], {n, 0, 11}, {m, 0, n}] // Flatten (* Roger L. Bagula, Sep 06 2008 *)
Formula
T(0, k)=T(n, 0)=1, T(n, k)=nk+0^n, n, k>0
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, Sep 06 2008
Comments