|
| |
|
|
A370846
|
|
a(n) = 5 + 4^n + 3*((-i*sqrt(7) - 3)^n + (i*sqrt(7) - 3)^n)/2^n.
|
|
0
|
|
|
|
0, 24, 96, 168, 1200, 3960, 16128, 66888, 259152, 1052184, 4195488, 16759272, 67158000, 268359864, 1073772096, 4295178888, 17179113360, 68720897880, 274876666848, 1099509663528, 4398057364272, 17592161341944, 70368774872448, 281474983436232, 1125899763886800
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
For n > 2 and n != 0 (mod 3), also the number of minimum vertex colorings in the n-antiprism graph.
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = 2*a(n-1) + 7*a(n-2) + 8*a(n-3) - 16*a(n-4).
G.f.: -24*x^2*(-1+2*x)*(1+4*x)/((-1+x)*(-1+4*x)*(1+3*x+4*x^2)).
|
|
|
MATHEMATICA
|
Table[5 + 4^n + 3 ((-I Sqrt[7] - 3)^n + (I Sqrt[7] - 3)^n)/2^n, {n, 25}]
LinearRecurrence[{2, 7, 8, -16}, {0, 24, 96, 168}, 20]
CoefficientList[Series[-(24 x (-1 + 2 x) (1 + 4 x)/((-1 + x) (-1 + 4 x) (1 + 3 x + 4 x^2))), {x, 0, 20}], x]
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
