|
|
A338153
|
|
a(n) is the number of acyclic orientations of the edges of the n-prism.
|
|
4
|
|
|
204, 1862, 14700, 109334, 790524, 5633222, 39828300, 280376054, 1968934044, 13807724582, 96754776300, 677686169174, 4745413960764, 33224340503942, 232596153986700, 1628276158432694, 11398345428510684, 79790067272259302, 558537067986067500, 3909785864202510614
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
3,1
|
|
COMMENTS
|
Conjectured linear recurrence and g.f. confirmed by Kagey's formula. - Ray Chandler, Mar 10 2024
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 2*x^3*(102 - 497*x + 742*x^2 - 392*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 7*x)).
a(n) = 14*a(n-1) - 63*a(n-2) + 106*a(n-3) - 56*a(n-4) for n>6.
(End)
a(n) = 5 + 7^n - 2^(n+1) - 2*4^n. - Peter Kagey, Nov 15 2020
|
|
EXAMPLE
|
For n = 4, the 4-prism is the 3-dimensional cube, so a(4) = A334247(3) = 1862.
|
|
MATHEMATICA
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|