|
| |
|
|
A173125
|
|
a(n) = Sum_{k == floor(n/2) (mod 5)} C(n,k).
|
|
2
|
|
|
|
1, 1, 2, 3, 6, 10, 20, 35, 70, 127, 254, 474, 948, 1807, 3614, 6995, 13990, 27370, 54740, 107883, 215766, 427351, 854702, 1698458, 3396916, 6765175, 13530350, 26985675, 53971350, 107746282, 215492564, 430470899, 860941798, 1720537327, 3441074654
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Greater of number of closed walks of length n from a node on a pentagon and number of walks of length n between two adjacent nodes on a pentagon.
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = 2*a(n-1)+3*a(n-2)-6*a(n-3)-a(n-4)+2*a(n-5). - Colin Barker, Sep 14 2014
G.f.: -(x-1)*(x^3+3*x^2-1) / ((2*x-1)*(x^2-x-1)*(x^2+x-1)). - Colin Barker, Sep 14 2014
|
|
|
EXAMPLE
|
For n=15, k=7 mod 5 gives k=2, 7 or 12, and C(15,2)+C(15,7)+C(15,12) = 105+6435+455, so a(15)=6995.
|
|
|
PROG
|
(PARI) Vec(-(x-1)*(x^3+3*x^2-1)/((2*x-1)*(x^2-x-1)*(x^2+x-1)) + O(x^100)) \\ Colin Barker, Sep 14 2014
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
