A127098 Triangle T(n,m) read by rows: product A127093 * A127094.

1, 5, 2, 10, 0, 3, 21, 2, 8, 4, 26, 0, 0, 0, 5, 50, 2, 3, 18, 12, 6, 50, 0, 0, 0, 0, 0, 7, 85, 2, 8, 4, 32, 0, 16, 8, 91, 0, 3, 0, 0, 0, 27, 0, 9, 130, 2, 0, 0, 5, 50, 0, 0, 20, 10, 122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 210, 2, 11, 22, 12, 6, 72, 0, 48, 36, 24, 12, 170, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 250, 2, 0, 0, 0, 0, 7, 98, 0

Offset: 1

Author

Gary W. Adamson, Jan 05 2007

Keywords

• nonn
• tabl
• easy

Comments

A127097 is a close companion.

Examples

			First few rows of the triangle are:
1;
5, 2;
10, 0, 3;
21, 2, 8, 4;
26, 0, 0, 0, 5;
50, 2, 3, 18, 12, 6;
50, 0, 0, 0, 0, 0, 7;
85, 2, 8, 4, 32, 0, 16, 8;
		

Crossrefs

Cf. A127097, A127093, A127094, A001001, A001157.

Programs

Maple

A127093 := proc(n,m) if m> n or m<1 or n < 1 then 0 ; elif (n mod m) = 0 then m; else 0 ; fi; end:
A127094 := proc(n,m) A127093(n,n-m+1) ; end: A127098 := proc(n,m) add( A127093(n,k)*A127094(k,m),k=1..n) ; end:
for n from 1 to 30 do for m from 1 to n do printf("%d,",A127098(n,m)) ; od: od: # R. J. Mathar, Mar 02 2009

Formula

T(n,m) = Sum_{k=m..n} A127093(n,k)*A127094(k,m).

Row sums: Sum_{m=1..n} T(n,m) = A001001(n).

Left column: T(1,m) = A001157(m).

Extensions

Edited and extended by R. J. Mathar, Mar 02 2009