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Search: id:A121544
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| A121544 |
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Sum of all proper base 4 numbers with n digits (those not beginning with 0). |
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+0
1
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| 6, 114, 1896, 30624, 491136, 7862784, 125822976, 2013241344, 32212156416, 515395682304
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Sum of the first 3*(4^(n-1)) integers starting with 4^(n-1). Sum of the integers from 4^(n-1) to (4^n)-1. First differences of A026337 4^n*(4^n-1)/2. cf. A007090 Numbers in base 4. 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) = (4^(n-1) + 4^n - 1) * 3 * (4^(n-1))/2.
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EXAMPLE
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a(1) = 6 = 1 + 2 + 3.
a(2) = 114 = 10_4 + 11_4 + 12_4 + 13_4 + 20_4 + 21_4 + 22_4 + 23_4 + 30_4 + 31_4 + 32_4 + 33_4 = (4+5+6+7+8+9+10+11+12+13+14+15)_10.
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CROSSREFS
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Cf. A007090, A010036, A026121, A026337, A101291.
Adjacent sequences: A121541 A121542 A121543 this_sequence A121545 A121546 A121547
Sequence in context: A066931 A051228 A059116 this_sequence A003425 A052465 A113015
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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 08 2006
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