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A028307 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. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Suggested by Problem 401 of the All-Soviet-Union Mathematical Competitions 1961-1986. Two different links are available for this collection.

LINKS

Table of n, a(n) for n=1..29.

Mauro Fiorentini, Further comments

Vladimir A. Pertsel, Problems of the All-Soviet-Union Mathematical Competitions 1961-1986

FORMULA

From A.H.M. Smeets, Feb 25 2022: (Start)

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)

EXAMPLE

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;

  ...

CROSSREFS

Cf. A028308, A062896, A340389.

Sequence in context: A182735 A135565 A139488 * A027298 A000236 A109327

Adjacent sequences:  A028304 A028305 A028306 * A028308 A028309 A028310

KEYWORD

nonn,nice

AUTHOR

Mauro Fiorentini

EXTENSIONS

More terms from the author, Jul 03 2001

STATUS

approved

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Last modified September 27 12:49 EDT 2022. Contains 357057 sequences. (Running on oeis4.)