|
|
A298567
|
|
a(n) = Sum_{k=0..2*n/3} C(n-k,2*k-n)^2.
|
|
1
|
|
|
1, 0, 1, 1, 1, 4, 2, 9, 10, 17, 37, 41, 102, 136, 251, 450, 667, 1325, 2011, 3658, 6246, 10293, 18686, 30461, 54183, 92169, 157438, 276414, 466579, 818256, 1400509, 2419379, 4202829, 7208342, 12556360, 21621891, 37480728, 64965461, 112227269
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 1/sqrt((1-x^2)^2+x^6-2*x^5-2*x^3).
D-finite with recurrence: n*a(n) -2*(n-1)*a(n-2)-(2*n-3)*a(n-3)+(n-2)*a(n-4) -(2*n-5)*a(n-5) +(n-3)*a(n-6) = 0. - R. J. Mathar, Jan 21 2020
|
|
MAPLE
|
option remember;
if n < 7 then
op(n+1, [1, 0, 1, 1, 1, 4, 2]) ;
else
-2*(n-1)*procname(n-2)-(2*n-3)*procname(n-3)+(n-2)*procname(n-4)
-(2*n-5)*procname(n-5)+(n-3)*procname(n-6) ;
-%/n ;
end if;
|
|
PROG
|
(Maxima)
a(n):=sum(binomial(n-k, 2*k-n)^2, k, 0, 2*n/3);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|