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A383581

a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * binomial(2*(n-3*k),n-3*k).

1, 2, 6, 21, 74, 270, 1005, 3788, 14418, 55289, 213270, 826614, 3216629, 12558928, 49175136, 193023965, 759299438, 2992534344, 11813985377, 46709675040, 184928644350, 733047010709, 2908981549006, 11555513379450, 45945148281437, 182835149061920, 728149606630164

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..400

FORMULA

G.f.: 1/sqrt((1 - x^3) * (1 - x^3 - 4*x)).

MATHEMATICA

Table[Sum[Binomial[n-2*k, k]* Binomial[2*(n-3*k), n-3*k], {k, 0, Floor[n/3]}], {n, 0, 30}] (* Vincenzo Librandi, May 02 2025 *)

PROG

(PARI) a(n) = sum(k=0, n\3, binomial(n-2*k, k)*binomial(2*(n-3*k), n-3*k));

(Magma) [&+[Binomial(n-2*k, k) * Binomial(2*(n-3*k), n-3*k): k in [0..n div 3]]: n in [0..25]]; // Vincenzo Librandi, May 02 2025