A144470 Triangle t(n,m) read by rows: t(n,m) = binomial(n,m)*3^m if m <= n/2, else t(n,m) = t(n,n-m).

1, 1, 1, 1, 6, 1, 1, 9, 9, 1, 1, 12, 54, 12, 1, 1, 15, 90, 90, 15, 1, 1, 18, 135, 540, 135, 18, 1, 1, 21, 189, 945, 945, 189, 21, 1, 1, 24, 252, 1512, 5670, 1512, 252, 24, 1, 1, 27, 324, 2268, 10206, 10206, 2268, 324, 27, 1, 1, 30, 405, 3240, 17010, 61236, 17010, 3240

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Oct 09 2008

Keywords

• nonn
• tabl
• easy

Comments

The row sums are 1, 2, 8, 20, 80, 212, 848, 2312, 9248, 25652, 102608, ...

Examples

			1;
1, 1;
1, 6, 1;
1, 9, 9, 1;
1, 12, 54, 12, 1;
1, 15, 90, 90, 15, 1;
1, 18, 135, 540, 135, 18, 1;
1, 21, 189, 945, 945, 189, 21, 1;
1, 24, 252, 1512, 5670, 1512, 252, 24, 1;
1, 27, 324, 2268, 10206, 10206, 2268, 324, 27, 1;
1, 30, 405, 3240, 17010, 61236, 17010, 3240, 405, 30, 1;
		

Programs

Maple

A144470 := proc(n,m) if m <= floor(n/2) then binomial(n,m)*3^m ; else procname(n,n-m) ; end if; end proc: # R. J. Mathar, Feb 03 2011

Mathematica

f[n_, m_] = If[m <= Floor[n/2], m, n - m]; Table[Table[Binomial[n, m]*3^f[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Formula

t(n,m) = binomial(n,m)*3^m if 0 <= m <= n/2, t(n,m) = binomial(n,m)*3^(n-m) if n/2 < m <= n.