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 A097074 Expansion of (1-x+2x^2)/((1-x)(1-x-2x^2)). 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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] LINKS 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). FORMULA 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] a(n) = A000975(n+1)-A000975(n)+2*A000975(n-1). - R. J. Mathar, Feb 27 2019 MATHEMATICA 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 *) CROSSREFS Sequence in context: A000323 A146131 A083943 * A050559 A082676 A146932 Adjacent sequences:  A097071 A097072 A097073 * A097075 A097076 A097077 KEYWORD easy,nonn AUTHOR Paul Barry, Jul 22 2004 EXTENSIONS Correction of the homogeneous recurrence and index link added. - Wolfdieter Lang, Nov 16 2013 STATUS approved

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Last modified January 19 18:52 EST 2022. Contains 350466 sequences. (Running on oeis4.)