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A175039 Minimum number of integer-sided squares needed to tile an n-row staircase (a figure with n unit squares in the n-th row, and the leftmost squares of each row vertically aligned). 0
1, 3, 3, 7, 6, 7, 7, 11, 12, 13, 12, 15, 14, 15, 15, 20, 20, 23, 22, 23, 24, 25, 24, 29, 28, 29, 28 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) >= n, since the rightmost squares in each row must be covered by distinct tiles.

a(n) = n iff n = 2^k - 1.

a(n) = n+1 iff n = 2^k - 2^m - 1.

LINKS

Table of n, a(n) for n=1..27.

Canadian Mathematical Society, 2010 Canadian Mathematical Olympiad, Problem 1

C. Zhang, Diagrams of tilings

EXAMPLE

See link for diagrams of tilings.

CROSSREFS

Solutions for a(n) = n: A000225. Solutions for a(n) = n+1: A030130, excluding 0.

Sequence in context: A200690 A045773 A256700 * A222405 A146970 A078708

Adjacent sequences:  A175036 A175037 A175038 * A175040 A175041 A175042

KEYWORD

nonn

AUTHOR

Cyril Zhang, Apr 04 2010

STATUS

approved

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Last modified March 26 23:19 EDT 2017. Contains 284141 sequences.