A157635 Triangle read by rows: T(n,m) = 1 if n*m*(n-m) = 0, and n*m*(n-m) otherwise.

1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 16, 12, 1, 1, 20, 30, 30, 20, 1, 1, 30, 48, 54, 48, 30, 1, 1, 42, 70, 84, 84, 70, 42, 1, 1, 56, 96, 120, 128, 120, 96, 56, 1, 1, 72, 126, 162, 180, 180, 162, 126, 72, 1, 1, 90, 160, 210, 240, 250, 240, 210, 160, 90, 1

Offset: 0

Author

Roger L. Bagula, Mar 03 2009

Keywords

• nonn
• tabl

Comments

Row sums are: {1, 2, 4, 14, 42, 102, 212, 394, 674, 1082, 1652, ...}.

Examples

			Triangle begins as:
   1;
   1,  1;
   1,  2,  1;
   1,  6,  6,  1;
   1, 12, 16, 12,  1;
   1, 20, 30, 30, 20,  1;
   1, 30, 48, 54, 48, 30, 1;
		

Links

• G. C. Greubel, Rows n = 0..100 of triangle, flattened

Programs

Magma

[[n*k*(n-k) eq 0 select 1 else n*k*(n-k): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Apr 09 2019

Mathematica

Table[If[n*m*(n-m)==0, 1, n*m*(n-m)], {n, 0, 10}, {m, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 09 2019 *)

PARI

{T(n,k) = if(n*k*(n-k)==0, 1, n*k*(n-k))}; \\ G. C. Greubel, Apr 09 2019

Sage

@CachedFunction
def T(n, k):
   if (n*k*(n-k)==0): return 1
   else: return n*k*(n-k)
[[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Apr 09 2019

Formula

T(n,m) = 1 if n*m*(n - m) = 0, and n*m*(n - m) otherwise.

Extensions

Edited by G. C. Greubel, Apr 09 2019