|
|
A099625
|
|
Sum C(n-k,k+2)2^(n-k-2)(1/2)^k, k=0..floor(n/2).
|
|
1
|
|
|
0, 0, 1, 6, 25, 88, 281, 842, 2413, 6692, 18101, 48014, 125393, 323376, 825393, 2088850, 5248853, 13110844, 32584653, 80639446, 198844281, 488813768, 1198491913, 2931934938, 7158830781, 17450923092, 42480107365, 103283553054
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
In general a(n)=sum{k=0..floor(n/2), C(n-k,k+2)u^(n-k-2)(v/u)^k has g.f. x^2/((1-u*x)^2(1-u*x-v*x^2)) and satisfies the recurrence a(n)=3u*a(n-1)-(3u^2-v)a(n-2)+(u^3-2uv)a(n-3)+u^2^v*a(n-4).
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x^2/((1-2x)^2(1-2x-x^2)); a(n)=sum{k=0..floor(n/2), C(n-k, k+2)2^(n-2k-2)}; a(n)=6a(n-1)-11a(n-2)+4a(n-3)+4a(n-4).
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|