A156664 Binomial transform of A052551.

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

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 A358464

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