login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A115730 a(n) = a(n-3)+A001654(n-1) with a(0)=0, a(1)=0 and a(2)=1. 5
0, 0, 1, 2, 6, 16, 42, 110, 289, 756, 1980, 5184, 13572, 35532, 93025, 243542, 637602, 1669264, 4370190, 11441306, 29953729, 78419880, 205305912, 537497856, 1407187656, 3684065112, 9645007681, 25250957930, 66107866110 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Old name was: Dihedral D2 elliptical invariant transform on A000045: a[n+1]/a[n]= 1+Phi=1+(1+Sqrt[5])/2.

The a(n+1) represent the Ca2 and Ze4 sums of the Golden Triangle A180662. Furthermore the a(3*n) represent the Ze1 (terms doubled) and Ca3 sums of the Golden triangle. See A180662 for more information about these and other triangle sums.

LINKS

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (2,2,0,-2,-2,1).

FORMULA

a(n) = -Floor[g[b[n+1]] where b[n]=A000045[n], g[x]=(x^2-1)^2/(-4*x^2).

G.f.: -x^2 / ( (x-1)*(1+x)*(1+x+x^2)*(x^2-3*x+1) ). - R. J. Mathar, Jun 20 2015

a(n)-a(n-2) = A182890(n-1). - R. J. Mathar, Jun 20 2015

MAPLE

nmax:=31: with(combinat): for n from 0 to nmax do A001654(n):=fibonacci(n) * fibonacci(n+1) od: a(0):=0: a(1):=0: a(2):=1: for n from 3 to nmax do a(n):=a(n-3) + A001654(n-1) od: seq(a(n), n=0..nmax);

MATHEMATICA

F[0] = 0; F[1] = 1; F[n_] := F[n] = F[n - 1] + F[n - 2] g[x_] = (x^2 - 1)^2/(-4*x^2) a = Table[ -Floor[g[F[n]]], {n, 1, 32}] Table[N[a[[n + 1]]/a[[n]]], {n, 1, Length[a] - 1}]

CROSSREFS

Cf. A001654, A000045, A079962, A064831, A180664, A180665, A180666.

Sequence in context: A156664 A025169 A111282 * A191694 A224232 A217661

Adjacent sequences:  A115727 A115728 A115729 * A115731 A115732 A115733

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Mar 13 2006

EXTENSIONS

Corrected and information added by Johannes W. Meijer, Sep 22 2010

Edited by Editors-in-Chief. - N. J. A. Sloane, Jun 20 2015

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 January 21 08:09 EST 2020. Contains 331104 sequences. (Running on oeis4.)