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A097074
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Expansion of (1-x+2x^2)/((1-x)(1-x-2x^2)).
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5
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1, 1, 5, 9, 21, 41, 85, 169, 341, 681, 1365, 2729, 5461, 10921, 21845, 43689, 87381, 174761, 349525, 699049, 1398101, 2796201, 5592405, 11184809, 22369621, 44739241, 89478485, 178956969, 357913941, 715827881, 1431655765, 2863311529
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OFFSET
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0,3
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COMMENTS
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Partial sums of A097073.
This is the sequence A(1,1;1,2;2) of the family of sequences [a,b:c,d:k] considered by G. Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. [From Wolfdieter Lang, Oct 18 2010]
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LINKS
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Table of n, a(n) for n=0..31.
Wolfdieter Lang, Notes on certain inhomogeneous three term recurrences. [From Wolfdieter Lang, Oct 18 2010]
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).
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FORMULA
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a(n)=2*A001045(n+1)-1; a(n)=4*2^n/3+2(-1)^n/3-1.
Contribution from Wolfdieter Lang, Oct 18 2010: (Start)
a(n) = a(n-1) + 2*a(n-2) + 2, a(0)=1, a(1)=1.
a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3), a(0)=1=a(1), a(2)=5. Observed by G. Detlefs. See the W. Lang link. (End)
a(n) = 3*a(n-1)-2*a(n-2)+4*(-1)^n [From Gary Detlefs Dec 19 2010]
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MATHEMATICA
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CoefficientList[Series[(1-x+2x^2)/((1-x)(1-x-2x^2)), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, 1, -2}, {1, 1, 5}, 40] (* Harvey P. Dale, Apr 09 2018 *)
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CROSSREFS
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Sequence in context: A000323 A146131 A083943 * A050559 A082676 A146932
Adjacent sequences: A097071 A097072 A097073 * A097075 A097076 A097077
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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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EXTENSIONS
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Correction of the homogeneous recurrence and index link added. - Wolfdieter Lang, Nov 16 2013
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STATUS
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approved
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