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A147597
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a(n) is the number whose binary representation is A138146(n).
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4
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1, 7, 31, 119, 455, 1799, 7175, 28679, 114695, 458759, 1835015, 7340039, 29360135, 117440519, 469762055, 1879048199, 7516192775, 30064771079, 120259084295, 481036337159, 1924145348615, 7696581394439, 30786325577735, 123145302310919, 492581209243655
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OFFSET
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1,2
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COMMENTS
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Bisection of A147596.
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5,-4).
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FORMULA
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From R. J. Mathar, Feb 05 2010: (Start)
a(n) = 5*a(n-1) - 4*a(n-2) for n>5.
G.f.: x*(2*x+1)*(2*x-1)*(4*x^2+2*x+1)/((4*x-1)*(1-x)). (End)
a(n) = 7*4^(n-2) + 7 for n>3. - Colin Barker, Nov 25 2016
E.g.f.: (7/16)*(16*exp(x) + exp(4*x)) -(119/16) -31*x/4 -7*x^2/2 -2*x^3/3. - G. C. Greubel, Oct 25 2022
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MATHEMATICA
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Table[FromDigits[#, 2] &@ If[n < 4, ConstantArray[1, 2 n - 1], Join[#, ConstantArray[0, 2 n - 7], #]] &@ ConstantArray[1, 3], {n, 25}] (* or *)
Rest@ CoefficientList[Series[x (2 x + 1) (2 x - 1) (4 x^2 + 2 x + 1)/((4 x - 1) (1 - x)), {x, 0, 25}], x] (* Michael De Vlieger, Nov 25 2016 *)
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PROG
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(PARI) Vec(x*(2*x+1)*(2*x-1)*(4*x^2+2*x+1)/((4*x-1)*(1-x)) + O(x^30)) \\ Colin Barker, Nov 25 2016
(Magma) [1, 7, 31] cat [7*(1+4^(n-2)): n in [4..40]]; // G. C. Greubel, Oct 25 2022
(SageMath)
def A147597(n): return 7*(1+4^(n-2)) -(119/16)*int(n==0) -(31/4)*int(n==1) -7*int(n==2) -4*int(n==3)
[A147597(n) for n in range(1, 41)] # G. C. Greubel, Oct 25 2022
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CROSSREFS
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Cf. A138146, A145641, A147537, A147538, A147539.
Cf. A147540, A147590, A147595, A147596.
Sequence in context: A091344 A032197 A114289 * A048775 A181951 A218963
Adjacent sequences: A147594 A147595 A147596 * A147598 A147599 A147600
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KEYWORD
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base,easy,nonn
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AUTHOR
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Omar E. Pol, Nov 08 2008
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EXTENSIONS
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More terms from R. J. Mathar, Feb 05 2010
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STATUS
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approved
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