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1, 3, 2, 6, 2, 3, 10, 2, 3, 4, 15, 2, 3, 4, 5, 21, 2, 3, 4, 5, 6, 28, 2, 3, 4, 5, 6, 7, 36, 2, 3, 4, 5, 6, 7, 8, 45, 2, 3, 4, 5, 6, 7, 8, 9, 55, 2, 3, 4, 5, 6, 7, 8, 9, 10, 66, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 78, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 91, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Row sums = A028387.
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LINKS
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G. C. Greubel, Rows n = 1..100 of triangle, flattened
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FORMULA
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T(n,k) = A000012(n,k) * A127648(n,k) * A103451(n,k) as infinite lower triangular matrices. Replace left border of 1's in A002260 with (1, 3, 6, 10, 15,...).
T(n, k) = k with T(n,1) = binomial(n+1, 2). - G. C. Greubel, Nov 20 2019
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EXAMPLE
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First few rows of the triangle are:
1;
3, 2;
6, 2, 3;
10, 2, 3, 4;
15, 2, 3, 4, 5;
...
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MAPLE
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seq(seq( `if`(k=1, binomial(n+1, 2), k), k=1..n), n=1..15); # G. C. Greubel, Nov 20 2019
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k==1, Binomial[n+1, 2], k]; Table[T[n, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Nov 20 2019 *)
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PROG
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(PARI) T(n, k) = if(k==1, binomial(n+1, 2), k); \\ G. C. Greubel, Nov 20 2019
(MAGMA) [k eq 1 select Binomial(n+1, 2) else k: k in [1..n], n in [1..15]]; // G. C. Greubel, Nov 20 2019
(Sage)
@CachedFunction
def T(n, k):
if (k==1): return binomial(n+1, 2)
else: return k
[[T(n, k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Nov 20 2019
(GAP)
T:= function(n, k)
if k=1 then return Binomial(n+1, 2);
else return k;
fi; end;
Flat(List([1..15], n-> List([1..n], k-> T(n, k) ))); # G. C. Greubel, Nov 20 2019
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CROSSREFS
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Cf. A002260, A103451, A127648.
Sequence in context: A188614 A290798 A133519 * A143310 A131897 A061187
Adjacent sequences: A135220 A135221 A135222 * A135224 A135225 A135226
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson, Nov 23 2007
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EXTENSIONS
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More terms added by G. C. Greubel, Nov 20 2019
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STATUS
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approved
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