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).

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

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

a(n) <= A003817(n). - Austin Shapiro, Dec 29 2022

Links

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

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