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A028307
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Form a triangle with n numbers in top row; all other numbers are the sum of their parents. E.g.: 4 1 2 7; 5 3 9; 8 12; 20. The numbers must be positive and distinct and the final number is to be minimized. Sequence gives final number.
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5
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1, 3, 8, 20, 43, 98, 212, 465, 1000, 2144, 4497, 9504, 19872, 41455, 85356, 178630, 363467, 757085, 1541998, 3183600, 6515066, 13357593, 27432649, 55914902, 114683858, 233517515, 478061719, 972479046, 1986013932
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OFFSET
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1,2
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COMMENTS
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Suggested by Problem 401 of the All-Soviet-Union Mathematical Competitions 1961-1986. Two different links are available for this collection.
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LINKS
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FORMULA
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a(n) > 2*a(n-1). Proof: Let x, y be the numbers in the second last row, then x >= a(n-1), y >= a(n-1) and x != y, so a(n) = x + y > 2*a(n-1).
It seems that a(n) > (4/3)*(2*a(n-1)-a(n-2)). (End)
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EXAMPLE
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Solutions for n = 1, 2, ... are:
1;
1, 2;
2, 1, 4;
4, 1, 2, 7;
7, 2, 1, 4, 6;
8, 6, 1, 3, 2, 10;
...
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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More terms from the author, Jul 03 2001
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STATUS
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approved
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