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A174192 Expansion of (1-x+2x^2)/ ((1-x)*(1-2x-x^2)). 1
1, 2, 7, 18, 45, 110, 267, 646, 1561, 3770, 9103, 21978, 53061, 128102, 309267, 746638, 1802545, 4351730, 10506007, 25363746, 61233501, 147830750, 356895003, 861620758, 2080136521, 5021893802, 12123924127 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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)=-1+[1+sqrt(2)]^n+[1-sqrt(2)]^n+(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 = 7

a(3) = 2*a(2)+a(1)+2 = 2*7+2+2 = 18.

MATHEMATICA

CoefficientList[Series[(1-x+2x^2)/((1-x)*(1-2x-x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, -1, -1}, {1, 2, 7}, 30] (* Harvey P. Dale, Jul 18 2019 *)

CROSSREFS

Cf. A174191, A048655 (first differences)

Sequence in context: A037294 A076857 A243717 * A247289 A161870 A072338

Adjacent sequences:  A174189 A174190 A174191 * A174193 A174194 A174195

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 11 2010

EXTENSIONS

Terms corrected by R. J. Mathar, Oct 26 2011

STATUS

approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)