|
| |
|
|
A099176
|
|
a(n)=2a(n-1)+4a(n-2)-4a(n-3)-4a(n-4).
|
|
2
| |
|
|
1, 1, 4, 8, 24, 60, 168, 448, 1232, 3344, 9152, 24960, 68224, 186304, 509056, 1390592, 3799296, 10379520, 28357632, 77473792, 211662848, 578272256, 1579870208, 4316282880, 11792306176, 32217174016, 88018960384, 240472260608
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Form the 6 node graph with matrix A=[1,1,1,1,0,0; 1,1,0,0,1,1; 1,0,0,0,0,0; 1,0,0,0,0,0; 0,1,0,0,0,0; 0,1,0,0,0,0]. Then A099176 counts closed walks of length n at either of the degree 5 vertices.
|
|
|
FORMULA
| G.f.: (1-x-2x^2)/((1-2x^2)(1-2x-2x^2)) a(n)=(3+sqrt(3))(1+sqrt(3))^n/12+(3-sqrt(3))(1-sqrt(3))^n/12+2^((n-4)/2)(1+(-1)^n) a(n)=A002605(n)/2+2^((n-4)/2)(1+(-1)^n).
|
|
|
CROSSREFS
| Cf. A099177.
Sequence in context: A115641 A153334 A159612 * A190156 A116556 A010366
Adjacent sequences: A099173 A099174 A099175 * A099177 A099178 A099179
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 02 2004
|
| |
|
|
