|
|
A359620
|
|
Number of edge cuts in the n-antiprism graph.
|
|
2
|
|
|
1, 4, 62, 1440, 30346, 589556, 10858046, 192811016, 3336192082, 56642890908, 948242161382, 15706527467824, 258068117928826, 4214126476848580, 68489478048350222, 1109069751830483544, 17909240724783047842, 288575383662532867820, 4642173797092097149238
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The n-antiprism graph is defined for n >= 3. The sequence has been extrapolated to n = 0 using the recurrence. - Andrew Howroyd, Jan 26 2023
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Edge Cut
|
|
FORMULA
|
G.f.: (1 - 38*x + 511*x^2 - 2336*x^3 + 704*x^4 + 512*x^5 + 16*x^6)/((1 - x)^2*(1 - 16*x)*(1 - 12*x + 4*x^2)^2). - Andrew Howroyd, Jan 26 2023
|
|
MATHEMATICA
|
Table[2 + 16^n - 2^(n + 1) ChebyshevT[n, 3] + (6 - 2^(n + 1) (Fibonacci[2 n, 2] + 3 Fibonacci[2 n - 1, 2])) n/7, {n, 10}] // Expand (* Eric W. Weisstein, Mar 07 2023 *)
LinearRecurrence[{42, -617, 3640, -7144, 5888, -2064, 256}, {1, 4, 62, 1440, 30346, 589556, 10858046}, 20] (* Eric W. Weisstein, Mar 07 2023 *)
|
|
PROG
|
(PARI) Vec((1 - 38*x + 511*x^2 - 2336*x^3 + 704*x^4 + 512*x^5 + 16*x^6)/((1 - x)^2*(1 - 16*x)*(1 - 12*x + 4*x^2)^2) + O(x^21)) \\ Andrew Howroyd, Jan 26 2023
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
a(0)-(2) prepended and terms a(7) and beyond from Andrew Howroyd, Jan 26 2023
|
|
STATUS
|
approved
|
|
|
|