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A375307
a(n) = Sum_{k=0..floor(3*n/5)} binomial(3*n-3*k,2*k).
1
1, 1, 4, 16, 52, 194, 685, 2452, 8771, 31327, 112004, 400285, 1430710, 5113647, 18277014, 65325542, 233485250, 834519021, 2982723523, 10660798289, 38103641048, 136189372297, 486765693153, 1739789499591, 6218325456983, 22225431015537, 79437750107600
OFFSET
0,3
FORMULA
a(n) = A116090(2*n).
a(n) = 2*a(n-1) + 5*a(n-2) + 3*a(n-3) - 3*a(n-4) + a(n-5).
G.f.: (1 - x - 3*x^2)/(1 - 2*x - 5*x^2 - 3*x^3 + 3*x^4 - x^5).
PROG
(PARI) a(n) = sum(k=0, 3*n\5, binomial(3*n-3*k, 2*k));
(PARI) my(N=30, x='x+O('x^N)); Vec((1-x-3*x^2)/(1-2*x-5*x^2-3*x^3+3*x^4-x^5))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 11 2024
STATUS
approved