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A097074 Expansion of (1-x+2x^2)/((1-x)(1-x-2x^2)). 5
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

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).

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]

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 February 19 03:37 EST 2018. Contains 299330 sequences. (Running on oeis4.)