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A371456
Expansion of 1/(1 - x/(1 - 9*x^2)^(1/3)).
3
1, 1, 1, 4, 7, 28, 58, 223, 505, 1876, 4498, 16255, 40576, 143422, 368965, 1280830, 3373225, 11536309, 30958240, 104559082, 284934754, 952183048, 2628211291, 8703329266, 24283705558, 79785964555, 224677646416, 733160045533, 2081054132179, 6750196280983
OFFSET
0,4
FORMULA
a(n) = Sum_{k=0..floor(n/2)} 9^k * binomial((n+k)/3-1,k).
D-finite with recurrence -(n-1)*(n-2)*(n-8)*a(n) +3*(9*n^3-123*n^2+490*n-616)*a(n-2) +(n-1)*(n-2)*(n-8)*a(n-3) +9*(-27*n^3+441*n^2-2318*n+3984)*a(n-4) +6*(-3*n^3+45*n^2-206*n+284)*a(n-5) +81*(3*n-20)*(n-6)*(3*n-19)*a(n-6) +9*(3*n-20)*(n-6)*(3*n-19)*a(n-7)=0. - R. J. Mathar, Jun 07 2024
a(n) == 1 (mod 3). - Seiichi Manyama, Jun 11 2024
MAPLE
A371456 := proc(n)
add(9^k*binomial((n+k)/3-1, k), k=0..floor(n/2)) ;
end proc:
seq(A371456(n), n=0..70) ; # R. J. Mathar, Jun 07 2024
PROG
(PARI) a(n) = sum(k=0, n\2, 9^k*binomial((n+k)/3-1, k));
CROSSREFS
Cf. A373543.
Sequence in context: A061668 A239025 A339393 * A128386 A149074 A149075
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 07 2024
STATUS
approved