A109672 Entries in 3-dimensional solids related to Prouhet-Tarry problem.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 3, 3, 1, 3, 6, 3, 3, 3, 1, 1, 2, 1, 1, 5, 5, 1, 2, 5, 2, 1, 1, 1, 1, 2, 5, 2, 1, 5, 5, 1, 1, 2, 1, 1, 3, 3, 3, 6, 3, 1, 3, 3, 1, 1, 4, 6, 4, 1, 4, 12, 12, 4, 6, 12, 6, 4, 4, 1, 1, 3, 3, 1, 1, 7, 12, 7, 1, 3, 12

Offset: 0

Author

Philippe Deléham, Aug 07 2005

Keywords

• nonn
• tabf
• easy

Comments

Table of slices [n,k] of solids, read by antidiagonals, each slice [n,k] read by rows.

Slice [n,0] gives A046816.

Slice [0,k] gives A109649.

Slice [n,n] gives A109673.

Examples

			Slice [0,0]:
...1...
Slice [0,1]:
... 1 1 ...
.... 1 ....
Slice [1,0]:
.... 1 ....
... 1 1...
Slice [0,2]:
.. 1 2 1 ...
.... 2 2 ...
..... 1 .....
Slice [1,1]:
... 1 1 ...
.. 1 3 1..
... 1 1 ...
Slice [2,0]:
..... 1 .....
.... 2 2 ...
.. 1 2 1 ...
Slice [0,3]:
.. 1 3 3 1 ...
... 3 6 3 ....
.... 3 3 ......
..... 1 ........
Slice [1,2]:
... 1 2 1 ...
.. 1 5 5 1 ...
... 2 5 2 ...
.... 1 1 ...
Slice [2,1]:
.... 1 1 ...
... 2 5 2 ...
.. 1 5 5 1 ...
... 1 2 1 ...
Slice [3,0]:
..... 1 .....
.... 3 3 ....
... 3 6 3 ...
.. 1 3 3 1 ...
		

Formula

Sum of terms in 2D slice [n, k] is 3^(n+k); example : 1+2+1+1+5+5+1+2+5+2+1+127=3^(2+1) for slice [1, 2].