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A244663
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Binary representation of 4^n + 2^(n+1) - 1.
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2
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111, 10111, 1001111, 100011111, 10000111111, 1000001111111, 100000011111111, 10000000111111111, 1000000001111111111, 100000000011111111111, 10000000000111111111111, 1000000000001111111111111, 100000000000011111111111111, 10000000000000111111111111111
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = -1/9+10^(1+n)/9+100^n.
a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3).
G.f.: -x*(2000*x^2-2210*x+111) / ((x-1)*(10*x-1)*(100*x-1)).
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EXAMPLE
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a(3) is 1001111 because A093069(3) = 79 which is 1001111 in base 2.
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MAPLE
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MATHEMATICA
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LinearRecurrence[{111, -1110, 1000}, {111, 10111, 1001111}, 20] (* Harvey P. Dale, Dec 11 2014 *)
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PROG
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(PARI) vector(100, n, -1/9+10^(1+n)/9+100^n)
(PARI) Vec(-x*(2000*x^2-2210*x+111)/((x-1)*(10*x-1)*(100*x-1)) + O(x^100))
(Magma) [-1/9 + 10^(1 + n)/9 + 100^n : n in [1..15]]; // Wesley Ivan Hurt, Jul 09 2014
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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STATUS
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approved
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