

A179259


Arises in covering a graph by forests and a matching.


1



2, 12, 52, 140, 294, 532, 872, 1332, 1930, 2684, 3612, 4732, 6062, 7620, 9424, 11492, 13842, 16492, 19460, 22764, 26422, 30452, 34872, 39700, 44954, 50652, 56812, 63452, 70590, 78244, 86432, 95172, 104482, 114380, 124884, 136012, 147782
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

Kaiser proves that for any positive integer k and for epsilson = 1/((k+2)(3k^2+1)), the edges of any graph whose fractional arboricity is at most k + epsilon can be decomposed into $k$ forests and a matching.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Tomas Kaiser, Mickael Montassier, Andre Raspaud, Covering a graph by forests and a matching, Jul 02, 2010.
Index entries for linear recurrences with constant coefficients, signature (4,6,4,1).


FORMULA

a(n) = (n+2)*(3*n^2+1).
G.f.: 2*(12*x8*x^2+2*x^3)/(x1)^4. a(n) = +4*a(n1) 6*a(n2) +4*a(n3) a(n4). a(n) = 0 (mod 2). [From R. J. Mathar, Jul 08 2010]


EXAMPLE

a(4) = (4+2)*(3*4^2+1) = 294.


MATHEMATICA

CoefficientList[Series[2*(12*x8*x^2+2*x^3)/(x1)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 04 2012 *)


PROG

(MAGMA) I:=[2, 12, 52, 140]; [n le 4 select I[n] else 4*Self(n1)6*Self(n2)+4*Self(n3)Self(n4): n in [1..50]]; // Vincenzo Librandi, Jul 04 2012


CROSSREFS

Sequence in context: A043007 A300572 A176580 * A261474 A080675 A218782
Adjacent sequences: A179256 A179257 A179258 * A179260 A179261 A179262


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Jul 05 2010


STATUS

approved



