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A026581 Expansion of (1 + 2*x) / (1 - x - 4*x^2). 9
1, 3, 7, 19, 47, 123, 311, 803, 2047, 5259, 13447, 34483, 88271, 226203, 579287, 1484099, 3801247, 9737643, 24942631, 63893203, 163663727, 419236539, 1073891447, 2750837603, 7046403391, 18049753803, 46235367367, 118434382579, 303375852047, 777113382363 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

T(n,0) + T(n,1) + ... + T(n,2n), T given by A026568.

Row sums of Riordan array ((1+2x)/(1+x),x(1+2x)/(1+x)). Binomial transform is A055099. - Paul Barry, Jun 26 2008

Equals row sums of triangle A153341. - Gary W. Adamson, Dec 24 2008

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,4).

FORMULA

G.f.: (1 + 2*x) / (1 - x - 4*x^2).

a(n) = a(n-1) + 4*a(n-2), n>1.

a(n) = 2*A006131(n-1) + A006131(n), n>0.

a(n) = (2^(-1-n)*((1-sqrt(17))^n*(-5+sqrt(17)) + (1+sqrt(17))^n*(5+sqrt(17))))/sqrt(17). - Colin Barker, Dec 22 2016

MATHEMATICA

CoefficientList[Series[(1+2x)/(1-x-4x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{1, 4}, {1, 3}, 30] (* Harvey P. Dale, Aug 04 2015 *)

PROG

(PARI) Vec((1+2*x) / (1-x-4*x^2) + O(x^40)) \\ Colin Barker, Dec 22 2016

CROSSREFS

Cf. A006131, A026568, A026583, A026597, A026599, A052923, A055099.

Cf. A153341. - Gary W. Adamson, Dec 24 2008

Sequence in context: A029855 A209397 A110014 * A151535 A181360 A001372

Adjacent sequences:  A026578 A026579 A026580 * A026582 A026583 A026584

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Edited by Ralf Stephan, Jul 20 2013

STATUS

approved

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Last modified October 20 07:17 EDT 2018. Contains 316378 sequences. (Running on oeis4.)