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A135577
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Numbers that have only the digit "1" as first, central and final digit. For numbers with 5 or more digits the rest of digits are "0".
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15
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1, 111, 10101, 1001001, 100010001, 10000100001, 1000001000001, 100000010000001, 10000000100000001, 1000000001000000001, 100000000010000000001, 10000000000100000000001
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OFFSET
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1,2
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COMMENTS
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Also, equal to A135576(n), written in base 2.
a(n) has 2n-1 digits.
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LINKS
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FORMULA
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a(n) = A135576(n), written in base 2.
Also, a(1)=1, for n>1; a(n)=(concatenation of 1, n-2 digits 0, 1, n-2 digits 0 and 1).
a(n) = 1 + 10^(n-1) + 100^(n-1) for n>1.
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>4.
G.f.: x*(2000*x^3 - 1110*x^2 + 1) / ((1-x)*(10*x-1)*(100*x-1)). (End)
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EXAMPLE
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----------------------------
n ............ a(n)
----------------------------
1 ............. 1
2 ............ 111
3 ........... 10101
4 .......... 1001001
5 ......... 100010001
6 ........ 10000100001
7 ....... 1000001000001
8 ...... 100000010000001
9 ..... 10000000100000001
10 ... 1000000001000000001
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MATHEMATICA
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Join[{1}, LinearRecurrence[{111, -1110, 1000}, {111, 10101, 1001001}, 25]] (* G. C. Greubel, Oct 19 2016 *)
Join[{1}, Table[FromDigits[Join[{1}, PadRight[{}, n, 0], {1}, PadRight[{}, n, 0], {1}]], {n, 0, 10}]] (* Harvey P. Dale, Aug 15 2022 *)
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PROG
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(PARI) Vec(-x*(2000*x^3-1110*x^2+1)/((x-1)*(10*x-1)*(100*x-1)) + O(x^100)) \\ Colin Barker, Sep 16 2013
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CROSSREFS
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KEYWORD
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nonn,base,less,easy
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AUTHOR
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STATUS
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approved
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