A226583 Smallest number of integer-sided squares needed to tile a 10 X n rectangle.
0, 10, 5, 6, 4, 2, 4, 6, 5, 6, 1, 6, 5, 7, 5, 3, 5, 7, 6, 7, 2, 7, 6, 8, 6, 4, 6, 8, 7, 8, 3, 8, 7, 9, 7, 5, 7, 9, 8, 9, 4, 9, 8, 10, 8, 6, 8, 10, 9, 10, 5, 10, 9, 11, 9, 7, 9, 11, 10, 11, 6, 11, 10, 12, 10, 8, 10, 12, 11, 12, 7, 12, 11, 13, 11, 9, 11, 13, 12
Offset: 0
Examples
a(22) = 6: ._._._._._._._._._._._._._._._._._._._._._._. | | | | | | | | | | | | | | | | | | | | | |___________|___________| | | | | | | | | | | | | | | | |___________________|_______|_______|_______|
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,1,0,-1)
Programs
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Maple
a:= n-> `if`(n in [1, 2], 10/n, iquo(n, 10, 'r')+ [0, 5, 4, 6, 4, 2, 4, 6, 5, 6][r+1]): seq(a(n), n=0..100);
Formula
G.f.: x*(x^8+5*x^7-x^6-10*x^5-4*x^4-x^3-4*x^2+5*x+10) / (x^7-x^5-x^2+1).
a(n) = 1 + a(n-10) for n>12.