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A142586 Binomial transform of A014217. 2
1, 2, 5, 14, 39, 107, 290, 779, 2079, 5522, 14615, 38579, 101634, 267347, 702455, 1844114, 4838079, 12686507, 33254210, 87141659, 228301839, 598026002, 1566300455, 4101923939, 10741568514, 28126975907, 73647747815, 192833044754, 504884940879, 1321888886747 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The second term in the k-th iterated differences is 2, 3, 6, 10, 17, 28, 46, ... = A001610(k+1).

LINKS

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

Nickolas Hein, Jia Huang, Variations of the Catalan numbers from some nonassociative binary operations, arXiv:1807.04623 [math.CO], 2018.

Index entries for linear recurrences with constant coefficients, signature (5,-7,2).

FORMULA

G.f.: (1-3x+2x^2+x^3)/((1-3x+x^2)(1-2x)). a(n)=A005248(n)-2^(n-1), n>0. - R. J. Mathar, Sep 22 2008

a(0)=1, a(1)=2, a(2)=5, a(3)=14, a(n)=5*a(n-1)-7*a(n-2)+2*a(n-3). - Harvey P. Dale, Aug 08 2011

a(n) = (-2^(-1+n) + ((3-sqrt(5))/2)^n + ((3+sqrt(5))/2)^n) for n>0. - Colin Barker, Jun 05 2017

MATHEMATICA

CoefficientList[Series[(1-3x+2x^2+x^3)/((1-3x+x^2)(1-2x)), {x, 0, 30}], x] (* or *) Join[{1}, LinearRecurrence[{5, -7, 2}, {2, 5, 14}, 30]] (* Harvey P. Dale, Aug 08 2011 *)

PROG

(PARI) Vec((1-3*x+2*x^2+x^3)/((1-3*x+x^2)*(1-2*x)) + O(x^30)) \\ Colin Barker, Jun 05 2017

CROSSREFS

Sequence in context: A331573 A141752 A291729 * A202207 A132834 A000641

Adjacent sequences:  A142583 A142584 A142585 * A142587 A142588 A142589

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Sep 21 2008

EXTENSIONS

Edited and extended by R. J. Mathar, Sep 22 2008

STATUS

approved

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Last modified January 25 07:51 EST 2020. Contains 331241 sequences. (Running on oeis4.)