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A157635
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Triangle read by rows: T(n,m) = 1 if n*m*(n-m) = 0, and n*m*(n-m) otherwise.
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2
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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
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table;
graph;
refs;
listen;
history;
text;
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OFFSET
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0,5
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COMMENTS
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Row sums are: {1, 2, 4, 14, 42, 102, 212, 394, 674, 1082, 1652, ...}.
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LINKS
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FORMULA
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T(n,m) = 1 if n*m*(n - m) = 0, and n*m*(n - m) otherwise.
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EXAMPLE
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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;
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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