|
| |
|
|
A100304
|
|
Expansion of (1-x-6x^2)/(1-x-8x^2).
|
|
1
| |
|
|
1, 0, 2, 2, 18, 34, 178, 450, 1874, 5474, 20466, 64258, 227986, 742050, 2565938, 8502338, 29029842, 97048546, 329287282, 1105675650, 3739973906, 12585379106, 42505170354, 143188203202, 483229566034, 1628735191650, 5494571719922
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Construct a graph as follows:form the graph whose adjacency matrix is the tensor product of that of P_3 and [1,1;1,1], then add a loop at each of the 'internal' nodes. (Spectrum : [0^3;1;(1-sqrt(33))/2;(1+sqrt(33))/2]). a(n) counts closed walks of length n at each of the extremity nodes. Partial sums are A100302.
|
|
|
FORMULA
| a(n)=3*0^n/4+(1/8-sqrt(33)/264)(1/2+sqrt(33)/2)^n+(1/8+sqrt(33)/264)(1/2-sqrt(33)/2)^n
|
|
|
CROSSREFS
| Cf. A100305.
Sequence in context: A055735 A168296 A205454 * A096190 A136434 A001183
Adjacent sequences: A100301 A100302 A100303 * A100305 A100306 A100307
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Nov 12 2004
|
| |
|
|
