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 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 Table of n, a(n) for n=0..38. 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 Adjacent sequences: A298564 A298565 A298566 * A298568 A298569 A298570 KEYWORD nonn AUTHOR Vladimir Kruchinin, Jan 21 2018 STATUS approved

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Last modified June 8 08:52 EDT 2023. Contains 363162 sequences. (Running on oeis4.)