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A125682
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a(n) = (6^n - 1)*3/5.
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2
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3, 21, 129, 777, 4665, 27993, 167961, 1007769, 6046617, 36279705, 217678233, 1306069401, 7836416409, 47018498457, 282110990745, 1692665944473, 10155995666841, 60935974001049, 365615844006297, 2193695064037785, 13162170384226713, 78973022305360281
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OFFSET
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1,1
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COMMENTS
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The base-6 numbers 3_6, 33_6, 333_6, 3333_6, 33333_6, 333333_6, ... converted to base 10.
Also the total number of holes in a certain triangle fractal (start with 6 triangles, 3 holes) after n iterations. See illustration in Ngaokrajang link. - Jens Ahlström, Aug 29 2023
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LINKS
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FORMULA
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EXAMPLE
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Base 6 Base 10
3 ............. 3 = 3*6^0
33 ........... 21 = 3*6^1 + 3*6^0
333 ......... 129 = 3*6^2 + 3*6^1 + 3*6^0
3333 ........ 777 = 3*6^3 + 3*6^2 + 3*6^1 + 3*6^0, etc.
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MAPLE
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seq((6^n-1)*3/5, n=1..27);
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Definition rewritten (with Lajos formula) from Bruno Berselli, Apr 18 2012
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STATUS
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approved
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