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A026243 a(n) = A000522(n) - 2. 4
0, 3, 14, 63, 324, 1955, 13698, 109599, 986408, 9864099, 108505110, 1302061343, 16926797484, 236975164803, 3554627472074, 56874039553215, 966858672404688, 17403456103284419, 330665665962403998, 6613313319248079999, 138879579704209680020, 3055350753492612960483 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number of operations of addition and multiplication needed to evaluate a determinant of order n by cofactor expansion.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..170

C. Dubbs and D. Siegel, Computing determinants, College Math. J., 18 (1987), 48-49.

A. R. Pargeter, The vanishing coffee morning, Math. Gaz., 76 (1992), 386-387.

P. G. Sawtelle, The ubiquitous e, Math. Mag., 49 (1976), 244-245. [N. J. A. Sloane, Jan 29 2009]

FORMULA

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]

a(n) = floor(e*n!) - 2. - Bernard Schott, Apr 21 2019

EXAMPLE

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

MAPLE

a:= proc(n) a(n):= n*(a(n-1)+2)-1: end: a(1):= 0:

seq (a(n), n=1..30);  # Alois P. Heinz, May 25 2012

MATHEMATICA

Table[E*Gamma[n+1, 1] - 2, {n, 1, 30}] (* Jean-Fran├žois Alcover, May 18 2018 *)

CROSSREFS

Cf. A000522, A007526. Equals A033312 + A038156.

Cf. A001339.

Sequence in context: A242637 A151237 A151238 * A058139 A101476 A060801

Adjacent sequences:  A026240 A026241 A026242 * A026244 A026245 A026246

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, based on a message from a correspondent who wishes to remain anonymous, Dec 21 2003

STATUS

approved

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Last modified June 23 08:51 EDT 2021. Contains 345395 sequences. (Running on oeis4.)