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A329919
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a(n) is the total number of squares after n iterations of the "Square Multiscale" substitution.
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5
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1, 17, 33, 49, 65, 321, 337, 849, 865, 1633, 1649, 2673, 6769, 6785, 8065, 20353, 20369, 21905, 46481, 46497, 48289, 89249, 154785, 154801, 156849, 218289, 480433, 480449, 482753, 568769, 1224129, 1224145, 1226705, 1341393, 2652113, 3700689, 3700705, 3703521
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OFFSET
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0,2
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COMMENTS
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The substitution starts with a single square. Then that square is subdivided into a "ring" of 16 small squares surrounding a larger square as shown in the example. In subsequent iterations, the same subdivision is applied to the largest square(s) present in that iteration.
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LINKS
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EXAMPLE
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The basic subdivision rule:
---------------- ----------------
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| | ----------------
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| | ---- ----
| | ------> | | | |
| | ---- ----
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| | ----------------
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---------------- ----------------
n = 1: The initial substitution subdivides the single square into 1 large and 16 small squares (as shown in the diagram above), so a(1) = 17.
n = 2, 3, 4: The largest square present after the previous iterations is the center square, so 16 new squares are added in each of those iterations. Thus, a(2) = a(1) + 16 = 33, a(3) = a(2) + 16 = 49, a(4) = a(3) + 16 = 65.
n = 5: This iteration subdivides the 16 outer squares (shown in the diagram above). 16^2 = 256, so a(5) = a(4) + 256 = 321.
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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