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Search: id:A121515
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| A121515 |
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Sum of all proper ternary numbers with n digits (those not beginning with 0). |
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+0
1
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| 3, 33, 315, 26163, 235953, 2125035, 19129689, 172180323, 1549662273
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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First differences of A026121. A026121 is partial sums of a(n). Sum of the first 2*(3^(n-1)) integers starting with 3^n. cf. A010036 = Sum of all proper binary numbers with n digits (i.e. those not beginning with 0) = Sum of 2^n, ..., 2^(n+1) - 1 = 3*2^(2*n-3)-2^(n-2). cf. A101291 Sum of all numbers with n digits [base 10]. cf. A026121 3^n*(3^n-1)/2.
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FORMULA
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a(n) = (((3^n)*((3^n)-1)) - ((3^(n-1))*((3^(n-1)-1))))/2. a(n) = SUM[i=3^(n-1)..(3^n)-1]i.
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EXAMPLE
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a(1) = 3 = 1 + 2.
a(2) = 33 = 10_3 + 11_3 + 12_3 + 20_3 + 21_3 + 22_3 = 3+4+5+6+7.
a(3) = 315 = 100_3 + 101_3 + 102_3 + 110_3 + 111_3 + 112_3 + 120_3 + 121_3 + 122_3 + 200_3 + 201_3 + 202_3 + 210_3 + 211_3 + 212_3 + 220_3 + 221_3 + 222_3 = 9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26.
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CROSSREFS
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Cf. A010036, A026121, A101291.
Sequence in context: A107127 A135697 A097486 this_sequence A002277 A001507 A075835
Adjacent sequences: A121512 A121513 A121514 this_sequence A121516 A121517 A121518
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KEYWORD
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easy,nonn,base
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 07 2006
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