Start with a square; at each stage add a square at each expandable vertex so that the ratio between of the side of the squares at stage n+1 and at stage n is the golden ratio phi=0.618...; a(n) is the number of squares in a portion of the n-th stage (see below)
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The ratio phi=0.618... is chosen so that from the fourth stage on some squares overlap perfectly. The figure displays some kind of fractal behaviourbehavior. See illustration.
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1, 3, 10, 26, 63, 145, 332, 760, 1745, 4007, 9198, 21102, 48403, 111021, 254656, 584132, 1339893, 3073459, 7049906, 16171066, 37093175, 85084313, 195166404, 447672720, 1026871705, 2355438303, 5402904310, 12393181766, 28427480091, 65206953349, 149571708488
Colin Barker, <a href="/A269965/b269965.txt">Table of n, a(n) for n = 5..1000</a>
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Start with a square; at each stage add a square at each expandable vertex such so that the ratio between the side of the squares at stage n+1 and at stage n is the golden ratio phi=0.618...; a(n) is the number of squares in a portion of the n-th stage (see below)
a(n) counts is the number of squares colored red in the illustration.
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a(1)=a(2)=a(3)=a(4)=0, for n>= 5, a(n) = A269963(n-4)+a(n-1). a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) + 2*a(n-4) + 2*a(n-5) + 5.
a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) + 2*a(n-4) + 2*a(n-5) + 5.
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