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A298567
a(n) = Sum_{k=0..2*n/3} C(n-k,2*k-n)^2.
5
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
OFFSET
0,6
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
A298567 := proc(n)
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;
end proc: # R. J. Mathar, Jan 21 2020
PROG
(Maxima)
a(n):=sum(binomial(n-k, 2*k-n)^2, k, 0, 2*n/3);
CROSSREFS
Cf. A182878.
Sequence in context: A242049 A179398 A233295 * A006172 A171631 A052915
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Jan 21 2018
STATUS
approved