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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. a(2*k) <= 2*a(k) + 1, a(2*k+1) <= 2*a(k) + 1 for k >= 1. - Jinyuan Wang, Jul 17 2019 LINKS Canadian Mathematical Society, 2010 Canadian Mathematical Olympiad, Problem 1 C. Zhang, Diagrams of tilings [BROKEN LINK] 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,more AUTHOR Cyril Zhang, Apr 04 2010 STATUS approved

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Last modified October 6 03:55 EDT 2022. Contains 357261 sequences. (Running on oeis4.)