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A233774
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Total number of vertices in the first n rows of Sierpinski gasket, with a(0) = 1.
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9
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1, 3, 6, 10, 15, 19, 25, 33, 42, 46, 52, 60, 70, 78, 90, 106, 123, 127, 133, 141, 151, 159, 171, 187, 205, 213, 225, 241, 261, 277, 301, 333, 366, 370, 376, 384, 394, 402, 414, 430, 448, 456, 468, 484, 504, 520, 544, 576, 610, 618, 630, 646, 666, 682
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OFFSET
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0,2
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LINKS
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FORMULA
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EXAMPLE
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Illustration of initial terms:
-----------------------------------------------------
-----------------------------------------------------
* 0 1 1
/T\
*---* 1 2 3
/T\ /T\
*---*---* 2 3 6
/T\ /T\
*---* *---* 3 4 10
/T\ /T\ /T\ /T\
*---*---*---*---* 4 5 15
/T\ /T\
*---* *---* 5 4 19
-----------------------------------------------------
After five stages the number of "black" triangles in the structure is A006046(5) = 11. The total number of vertices is 19, so a(5) = 19.
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MATHEMATICA
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A233775[n_] := If[n == 0, 1, (2^IntegerExponent[n, 2]+1)*2^(DigitSum[n, 2]-1)];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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