A226581 Smallest number of integer-sided squares needed to tile an 8 X n rectangle.
0, 8, 4, 5, 2, 5, 4, 7, 1, 7, 5, 6, 3, 6, 5, 8, 2, 8, 6, 7, 4, 7, 6, 9, 3, 9, 7, 8, 5, 8, 7, 10, 4, 10, 8, 9, 6, 9, 8, 11, 5, 11, 9, 10, 7, 10, 9, 12, 6, 12, 10, 11, 8, 11, 10, 13, 7, 13, 11, 12, 9, 12, 11, 14, 8, 14, 12, 13, 10, 13, 12, 15, 9, 15, 13, 14, 11
Offset: 0
Examples
a(17) = 8: ._._._._._._._._._._._._._._._._._. | | | | | | | | | | | | | |_______| | | | |_________| | | | | | | | | |___| |_______________|_______|_____|_|_|
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1)
Programs
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Maple
a:= n-> `if`(n=1, 8, iquo(n, 8, 'r') +[0, 6, 4, 5, 2, 5, 4, 7][r+1]): seq(a(n), n=0..100);
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Mathematica
LinearRecurrence[{1,0,0,0,0,0,0,1,-1},{0,8,4,5,2,5,4,7,1,7,5},80] (* Harvey P. Dale, Sep 07 2016 *)
Formula
G.f.: x*(2*x^9-2*x^8-6*x^7+3*x^6-x^5+3*x^4-3*x^3+x^2-4*x+8) / (x^9-x^8-x+1).
a(n) = 1 + a(n-8) for n>9.