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A080521
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Triangle read by rows; n-th row contains the lexicographically first set of n distinct positive integers whose sum is 2^n.
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2
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2, 1, 3, 1, 2, 5, 1, 2, 3, 10, 1, 2, 3, 4, 22, 1, 2, 3, 4, 5, 49, 1, 2, 3, 4, 5, 6, 107, 1, 2, 3, 4, 5, 6, 7, 228, 1, 2, 3, 4, 5, 6, 7, 8, 476, 1, 2, 3, 4, 5, 6, 7, 8, 9, 979, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1993, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 4030
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OFFSET
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1,1
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LINKS
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FORMULA
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T(n,k) = k for 1 <= k < n;
T(n,n) = 2^n - n(n-1)/2. (End)
G.f.: x*y*(2 - x - 7*x*y + 4*x^2*y + 8*x^2*y^2 - 6*x^3*y^2 - 2*x^3*y^3 + 2*x^4*y^3)/((1-x*y)^3*(1-x)*(1-2*x*y)). - Robert Israel, Jul 04 2019
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EXAMPLE
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Triangle begins
2;
1, 3;
1, 2, 5;
1, 2, 3, 10;
1, 2, 3, 4, 22;
1, 2, 3, 4, 5, 49;
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MAPLE
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for n from 1 to 20 do
seq(k, k=1..n-1), 2^n-n*(n-1)/2
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MATHEMATICA
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Array[Join[Range[# - 1], {2^# - #*(# - 1)/2}] &, 15] // Flatten (* Paolo Xausa, Mar 16 2024 *)
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PROG
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(PARI) print(2, "; "); for(i=2, 20, s=0; for(j=1, i-1, print1(j, ", "); s+=j); print(2^i-s, "; ")) \\ Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jul 19 2005
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CROSSREFS
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First diagonal is A014844 (2^n - n(n-1)/2).
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jul 19 2005
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STATUS
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approved
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