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A157635 Triangle read by rows: T(n,m) = 1 if n*m*(n-m) = 0, and n*m*(n-m) otherwise. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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;

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 *)

PROG

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

(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

(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

CROSSREFS

Sequence in context: A168641 A255914 A143185 * A075798 A155864 A145903

Adjacent sequences:  A157632 A157633 A157634 * A157636 A157637 A157638

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Mar 03 2009

EXTENSIONS

Edited by G. C. Greubel, Apr 09 2019

STATUS

approved

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Last modified September 30 17:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)