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A375315
Expansion of (1 + x)/(1 - x^2*(1 + x)^3).
4
1, 1, 1, 4, 7, 11, 23, 45, 81, 154, 296, 555, 1046, 1986, 3753, 7085, 13404, 25348, 47904, 90568, 171245, 323728, 612009, 1157071, 2187496, 4135527, 7818464, 14781237, 27944604, 52830706, 99879234, 188826693, 356986401, 674901117, 1275934888, 2412219633, 4560424135
OFFSET
0,4
FORMULA
a(n) = a(n-2) + 3*a(n-3) + 3*a(n-4) + a(n-5).
a(n) = Sum_{k=0..floor(n/2)} binomial(3*k+1,n-2*k).
a(n) = A116090(n) + A116090(n-1).
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec((1+x)/(1-x^2*(1+x)^3))
(PARI) a(n) = sum(k=0, n\2, binomial(3*k+1, n-2*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 12 2024
STATUS
approved