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A186520 Number of evaluation schemes for x^n achieving the minimal number of multiplications, and with the maximal number of squarings among the multiplications. 0
1, 1, 1, 1, 1, 2, 4, 1, 1, 2, 4, 3, 5, 10, 2, 1, 1, 2, 4, 3, 5, 10, 2, 4, 7, 12, 2, 16, 47, 6, 22, 1, 1, 2, 4, 3, 5, 10, 10, 4, 6, 12, 2, 18, 2, 4, 10, 5, 7, 17, 2, 19, 55, 6, 28, 22, 49, 120, 8, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

For n=7, we can evaluate x^7 using only 4 operations in 6 ways:

  x^2 = x * x ; x^3 = x   * x^2 ; x^4 = x   * x^3 ; x^7 = x^3 * x^4    (1 squaring)

  x^2 = x * x ; x^3 = x   * x^2 ; x^4 = x^2 * x^2 ; x^7 = x^3 * x^4    (2 squarings)

  x^2 = x * x ; x^3 = x   * x^2 ; x^5 = x^2 * x^3 ; x^7 = x^2 * x^5    (1 squaring)

  x^2 = x * x ; x^3 = x   * x^2 ; x^6 = x^3 * x^3 ; x^7 = x   * x^6    (2 squarings)

  x^2 = x * x ; x^4 = x^2 * x^2 ; x^5 = x   * x^4 ; x^7 = x^2 * x^5    (2 squarings)

  x^2 = x * x ; x^4 = x^2 * x^2 ; x^6 = x^2 * x^4 ; x^7 = x   * x^6    (2 squarings)

The maximal number of squarings in these evaluation schemes is 2, and it is achieved by a(7) = 4 schemes.

CROSSREFS

Cf A003313, A186435, A186437.

Sequence in context: A188348 A336434 A007738 * A158570 A295224 A074749

Adjacent sequences:  A186517 A186518 A186519 * A186521 A186522 A186523

KEYWORD

nonn

AUTHOR

Laurent Thévenoux and Christophe Mouilleron, Feb 23 2011

EXTENSIONS

Example reformated by Christophe Mouilleron.

STATUS

approved

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Last modified June 16 04:56 EDT 2021. Contains 345056 sequences. (Running on oeis4.)