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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A124072 First differences of A129819. 3
0, 1, 0, 2, 1, 3, 1, 4, 2, 5, 2, 6, 3, 7, 3, 8, 4, 9, 4, 10, 5, 11, 5, 12, 6, 13, 6, 14, 7, 15, 7, 16, 8, 17, 8, 18, 9, 19, 9, 20, 10, 21, 10, 22, 11, 23, 11, 24, 12, 25, 12, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A129819 and its repeated differences are

0.0.1..1..3..4..7...8..12..14.19..21.27....

..0.1..0..2..1..3...1...4...2..5...2..6....

....1.-1..2.-1..2..-2...3..-2..3..-3..4....

......-2..3.-3..3..-4...5..-5..5..-6..7....

..........5.-6..6..-7...9.-10.10.-11.13...

...........-11.12.-13..16.-19.20.-21.24.-27

...............23.-25..29.-35.39.-41.45.-51

The left edge is A130668.

I discovered the array 1 1 -2 1 -3 2 in studying the singular points of planar polynomial differential systems (inspired by the reference).

LINKS

Table of n, a(n) for n=0..51.

Paul Curtz, Stabilite locale des systemes quadratiques, Ann. sc. Ecole Norm. Sup. vol 13 no 3 (1980) pp 293-302.

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

FORMULA

a(2n)=A004526(n). a(2n+1)=A000027(n+1) .

G.f.: x*(1+x^2+x^3)/((x^2+1)*(x-1)^2*(1+x)^2). [From R. J. Mathar, Feb 25 2009]

MATHEMATICA

a[n_?OddQ] := (n+1)/2; a[n_?EvenQ] := Floor[n^2/16] - Floor[(n-2)^2/16]; Table[a[n], {n, 0, 51}] (* Jean-Fran├žois Alcover, Aug 13 2012 *)

CROSSREFS

Sequence in context: A115118 A115121 A323523 * A189357 A100053 A029194

Adjacent sequences:  A124069 A124070 A124071 * A124073 A124074 A124075

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jun 26 2007

EXTENSIONS

Partially edited by R. J. Mathar, Jul 07 2008

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 26 04:27 EDT 2021. Contains 348256 sequences. (Running on oeis4.)