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A360890
G.f. satisfies A(x) = 1 + x/(1 - x^3) * A(x/(1 - x^3)).
4
1, 1, 1, 1, 2, 4, 7, 12, 25, 55, 115, 245, 564, 1331, 3103, 7407, 18388, 46198, 116503, 299966, 789426, 2095941, 5616114, 15299205, 42255533, 117689096, 331204936, 944052610, 2718150015, 7891518587, 23137661717, 68524545717, 204645635263, 616098009473
OFFSET
0,5
LINKS
FORMULA
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1-2*k,k) * a(n-1-3*k).
PROG
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\3, binomial(i-1-2*j, j)*v[i-3*j])); v;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 25 2023
STATUS
approved