

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
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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 293302.
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)*(x1)^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[(n2)^2/16]; Table[a[n], {n, 0, 51}] (* JeanFrançois 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



