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A174191 Expansion of (1+x)*(2*x-1)/((1-x)*(x^2+2*x-1)). 1
1, 2, 3, 6, 13, 30, 71, 170, 409, 986, 2379, 5742, 13861, 33462, 80783, 195026, 470833, 1136690, 2744211, 6625110, 15994429, 38613966, 93222359, 225058682, 543339721, 1311738122, 3166815963, 7645370046, 18457556053, 44560482150, 107578520351 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Pisano period lengths: 1, 2, 8, 4, 12, 8, 6, 8, 24, 12, 24, 8, 28, 6, 24, 16, 16, 24, 40, 12,.. (is this A175181?) - R. J. Mathar, Aug 10 2012

LINKS

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-1)

FORMULA

a(n)=2*a(n-1)+a(n-2)-2, with a(0)=1, a(1)=2.

a(n) = A052937(n-1), n>0. a(n)=3*a(n-1)-a(n-2)-a(n-3). [From R. J. Mathar, Mar 17 2010]

a(n)=1+(1/4)*sqrt(2)*{[1+sqrt(2)]^n-[1-sqrt(2)]^n}, with n>=0 [From Paolo P. Lava, Mar 17 2010]

EXAMPLE

a(2) = 2*a(1)+a(0)-2 = 2*2+1-2 = 3

a(3) = 2*a(2)+a(1)-2 = 2*3+2-2 = 6.

CROSSREFS

Cf. A174192, A001333 (first differences)

Sequence in context: A124682 A079512 A280746 * A052937 A005554 A316766

Adjacent sequences:  A174188 A174189 A174190 * A174192 A174193 A174194

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 11 2010

STATUS

approved

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Last modified October 22 00:52 EDT 2019. Contains 328315 sequences. (Running on oeis4.)