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

0,8

Comments

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

Links

Table of n, a(n) for n=0..84.

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

Example

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}

Mathematica

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, Sep 06 2008

Crossrefs

Sequence in context: A050935 A104769 A078013 * A047089 A122218 A072405

Adjacent sequences: A086458 A086459 A086460 * A086462 A086463 A086464

Keyword

easy,nonn,tabl

Author

Paul Barry, Jul 21 2003

Status

approved