A387482 a(n) = Sum_{k=0..floor(n/3)} 3^k * 2^(n-3*k) * binomial(k,n-3*k)^2.
1, 0, 0, 3, 6, 0, 9, 72, 36, 27, 486, 972, 297, 2592, 11664, 10611, 13446, 97200, 195129, 149688, 663876, 2334987, 2838726, 4697676, 21485817, 43705008, 51438240, 171480483, 517850982, 760446144, 1440329769, 5065354440, 10479570372, 15691149819, 44973017478
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Programs
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Magma
[(&+[3^k * 2^(n-3*k) * Binomial(k,n-3*k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // Vincenzo Librandi, Aug 31 2025
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Mathematica
Table[Sum[3^k* 2^(n-3*k)*Binomial[k,n-3*k]^2,{k,0,Floor[n/3]}],{n,0,40}] (* Vincenzo Librandi, Aug 31 2025 *) -
PARI
a(n) = sum(k=0, n\3, 3^k*2^(n-3*k)*binomial(k, n-3*k)^2);
Formula
G.f.: 1/sqrt((1-3*x^3-6*x^4)^2 - 72*x^7).