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A153435
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Numbers with 2n binary digits where every run length is 2, written in binary.
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8
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11, 1100, 110011, 11001100, 1100110011, 110011001100, 11001100110011, 1100110011001100, 110011001100110011, 11001100110011001100, 1100110011001100110011, 110011001100110011001100
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OFFSET
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1,1
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COMMENTS
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A043291 written in base 2.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (100,1,-100).
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FORMULA
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From Colin Barker, Apr 19 2014: (Start)
a(n) = (-101-99*(-1)^n+2^(3+2*n)*25^(1+n))/1818.
a(n) = 100*a(n-1)+a(n-2)-100*a(n-3).
G.f.: 11*x / ((x-1)*(x+1)*(100*x-1)).(End).
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EXAMPLE
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n ... a(n) ....... A043291(n)
1 ... 11 ............. 3
2 ... 1100 .......... 12
3 ... 110011 ........ 51
4 ... 11001100 ..... 204
5 ... 1100110011 ... 819
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MAPLE
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A153435:=n->(-101-99*(-1)^n+2^(3+2*n)*25^(1+n))/1818; seq(A153435(n), n=1..20); # Wesley Ivan Hurt, Apr 19 2014
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MATHEMATICA
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Table[(-101 - 99*(-1)^n + 2^(3 + 2*n)*25^(1 + n))/1818, {n, 20}] (* Wesley Ivan Hurt, Apr 19 2014 *)
CoefficientList[Series[11/((x - 1) (x + 1) (100 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 20 2014 *)
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PROG
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(PARI) Vec(11*x / ((x-1)*(x+1)*(100*x-1)) + O(x^100)) \\ Colin Barker, Apr 19 2014
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CROSSREFS
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Cf. A043291.
Sequence in context: A126197 A090814 A319424 * A266787 A109227 A133342
Adjacent sequences: A153432 A153433 A153434 * A153436 A153437 A153438
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KEYWORD
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easy,nonn,base
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AUTHOR
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Omar E. Pol, Dec 26 2008
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STATUS
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approved
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