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

Author

Gary W. Adamson, Feb 12 2009

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

Cf. A052551

Programs

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 *)

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

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

Extensions

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