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0, 3, 14, 63, 324, 1955, 13698, 109599, 986408, 9864099, 108505110, 1302061343, 16926797484, 236975164803, 3554627472074, 56874039553215, 966858672404688, 17403456103284419, 330665665962403998, 6613313319248079999, 138879579704209680020, 3055350753492612960483
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OFFSET
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1,2
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COMMENTS
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Number of operations of addition and multiplication needed to evaluate a determinant of order n by cofactor expansion.
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LINKS
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FORMULA
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a(n) = n*(a(n-1)+2)-1 for n>1, a(1) = 0. - Alois P. Heinz, May 25 2012
Conjecture: a(n) +(-n-2)*a(n-1) +(2*n-1)*a(n-2) +(-n+2)*a(n-3)=0. - R. J. Mathar, Jun 23 2013 [Confirmed by Altug Alkan, May 18 2018]
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EXAMPLE
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To calculate a determinant of order 3:
|a b c| |e f| |d f| |d e|
D = |d e f| = a * |h i| - b * |g i| + c * |g h| =
|g h i|
= a * (e*i - f*h) - b * (d*i - f*g) + c * (d*h - e*g).
There are 9 multiplications * and 5 additions (+ or -), so 14 operations and a(3) = 14. - Bernard Schott, Apr 21 2019
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MAPLE
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a:= proc(n) a(n):= n*(a(n-1)+2)-1: end: a(1):= 0:
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, based on a message from a correspondent who wishes to remain anonymous, Dec 21 2003
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STATUS
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approved
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