login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117202 Binomial transform of n*F(n). 3
0, 1, 4, 15, 52, 170, 534, 1631, 4880, 14373, 41810, 120406, 343884, 975325, 2749852, 7713435, 21540304, 59917826, 166094370, 458998523, 1264919720, 3477182961, 9536877614, 26102772910, 71309161752, 194468551225, 529490287924 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A045925.

Number of acyclic subgraphs of the wheel graph W_n (on n+1 vertices) with exactly n-1 edges. - Emil R. Vaughan, Jun 12 2007

Starting (1, 4, 15, 52, ...) = binomial transform of A136376: (1, 3, 8, 18, 37, ...). - Gary W. Adamson, Sep 03 2008

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..1000

J. Salas and A. D. Sokal, Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial, J. Stat. Phys. 135 (2009) 279-373, arXiv:0711.1738 [cond-mat.stat-mech]. Mentions this sequence. - N. J. A. Sloane, Mar 14 2014

Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1)

FORMULA

G.f.: x(1-2x+2x^2)/(1-3x+x^2)^2.

a(n) = 6a(n-1)-11a(n-2)+6a(n-3)-a(n-4).

a(n) = Sum_{k=0..n} C(n,k)*k*F(k).

From Benoit Cloitre, Nov 29 2006: (Start)

a(n) = Sum_[k=1..n} F(2k)*B(2n-2k)*binomial(2n,2k) where F=Fibonacci numbers and B=Bernoulli numbers;

a(n) = n*F(2n-1).

(End)

a(n) = (2^(-1-n)*(-(-5+sqrt(5))*(3+sqrt(5))^n + (3-sqrt(5))^n*(5+sqrt(5)))*n) / 5. - Colin Barker, Feb 26 2017

MATHEMATICA

Table[n Fibonacci[2n-1], {n, 0, 26}] (* or *) Table[Sum[Fibonacci[2k]*BernoulliB[2n-2k]*Binomial[2n, 2k], {k, 1, n}], {n, 0, 26}] (* or *) CoefficientList[Series[x(1-2x+2x^2)/(1-3x+x^2)^2 , {x, 0, 26}], x] (* Indranil Ghosh, Feb 26 2017 *)

PROG

(PARI) a(n) = n*fibonacci(2*n-1); \\ Indranil Ghosh, Feb 26 2017

(PARI) concat(0, Vec(x*(1-2*x+2*x^2) / (1-3*x+x^2)^2 + O(x^30))) \\ Colin Barker, Feb 26 2017

CROSSREFS

Cf. A001519, A111262.

Cf. A136376.

Sequence in context: A240365 A005492 A003013 * A291011 A137213 A027853

Adjacent sequences:  A117199 A117200 A117201 * A117203 A117204 A117205

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 02 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)