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A097072
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Expansion of (1 - 2*x + 2*x^2)/((1 - x^2)*(1 - 2*x)).
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3
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1, 0, 3, 4, 11, 20, 43, 84, 171, 340, 683, 1364, 2731, 5460, 10923, 21844, 43691, 87380, 174763, 349524, 699051, 1398100, 2796203, 5592404, 11184811, 22369620, 44739243, 89478484, 178956971, 357913940, 715827883, 1431655764, 2863311531
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OFFSET
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0,3
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1,-2)
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FORMULA
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a(n) = (4*2^n - 3 + 5*(-1)^n)/6.
a(n) = Sum_{k=0..n} (2^k - 1 + 0^k)(-1)^(n-k).
a(n) = A001045(n+1) - A000035(n).
a(n) = a(n-1) + 2*a(n-2) + 1, n > 1. - Gary Detlefs, Jun 20 2010
a(2*n) = A007583(n), a(2*n+1) = A080674(n), n >= 0. - Yosu Yurramendi, Feb 21 2017
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MATHEMATICA
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CoefficientList[Series[(1-2x+2x^2)/((1-x^2)(1-2x)), {x, 0, 50}], x] (* Harvey P. Dale, Mar 09 2011 *)
Table[2*2^n/3 - 1/2 + 5 (-1)^n/6, {n, 0, 32}] (* Michael De Vlieger, Feb 22 2017 *)
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PROG
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(PARI) for(n=0, 50, print1((4*2^n - 3 + 5*(-1)^n)/6, ", ")) \\ G. C. Greubel, Oct 10 2017
(MAGMA) [(4*2^n - 3 + 5*(-1)^n)/6: n in [0..50]]; // G. C. Greubel, Oct 10 2017
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CROSSREFS
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Cf. A000975.
Sequence in context: A222770 A036652 A295962 * A049977 A000677 A110865
Adjacent sequences: A097069 A097070 A097071 * A097073 A097074 A097075
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Jul 22 2004
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STATUS
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approved
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