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A156664 Binomial transform of A052551. 1
1, 2, 6, 16, 42, 108, 274, 688, 1714, 4244, 10458, 25672, 62826, 153372, 373666, 908896, 2207842, 5357348, 12988074, 31464568, 76179354, 184347564, 445923058, 1078290832, 2606699026, 6300077492, 15223631226, 36780894376, 88852528842, 214620169788 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-3,-2).

FORMULA

A007318 * A052551, where A052551 = (1, 1, 3, 3, 7, 7, 15, 15,...).

G.f.: (x^2 - 2*x + 1)/(2*x^3 + 3*x^2 - 4*x + 1). [Alexander R. Povolotsky, Feb 15 2009]

a(n) = 2*A000129(n+1)-2^n. [R. J. Mathar, Jun 15 2009]

a(n) = -2^n + (1-1/sqrt(2))*(1-sqrt(2))^n + (1+1/sqrt(2))*(1+sqrt(2))^n. - Alexander R. Povolotsky, Aug 16 2012

a(n+3) = -2*a(n) - 3*a(n+1) + 4*a(n+2). - Alexander R. Povolotsky, Aug 16 2012

EXAMPLE

a(3) = 16 = (1, 3, 3, 1) dot (1, 1, 3, 3) = (1 + 3 + 9 + 3).

MATHEMATICA

CoefficientList[Series[(x^2-2x+1)/(2x^3+3x^2-4x+1), {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -3, -2}, {1, 2, 6}, 40] (* Harvey P. Dale, Apr 20 2013 *)

PROG

(PARI) x='x+O('x^50); Vec((x^2-2*x+1)/(2*x^3+3*x^2-4*x+1)) \\ G. C. Greubel, Feb 24 2017

CROSSREFS

Cf. A052551

Sequence in context: A217194 A304662 A296625 * A025169 A111282 A115730

Adjacent sequences:  A156661 A156662 A156663 * A156665 A156666 A156667

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Feb 12 2009

EXTENSIONS

Corrected and extended by Harvey P. Dale, Apr 20 2013

STATUS

approved

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)