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URL: https://oeis.org/A390850

⇱ A390850 - OEIS


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A390850
a(n) = Sum_{k=0..n} (-1)^k * binomial(n+k-1,n-k) * Fibonacci(k+1).
2
1, -1, 0, 2, 3, 4, 9, 22, 48, 101, 216, 467, 1008, 2170, 4671, 10060, 21669, 46670, 100512, 216473, 466224, 1004119, 2162592, 4657618, 10031211, 21604436, 46529937, 100212518, 215829840, 464837341, 1001130120, 2156155339, 4643757840, 10001360522, 21540143943, 46391468444
OFFSET
0,4
FORMULA
G.f.: 1/(1+g-g^2), where g = x/(1-x)^2.
G.f.: (1 - x)^4 / (1 - 3*x + 3*x^2 - 3*x^3 + x^4).
a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3) - a(n-4) for n > 4.
MATHEMATICA
Table[Sum[(-1)^k*Binomial[n+k-1, n-k]*Fibonacci[k+1], {k, 0, n}], {n, 0, 40}] (* Vincenzo Librandi, Nov 26 2025 *)
PROG
(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+k-1, n-k)*fibonacci(k+1));
(Magma) [&+[(-1)^k*Binomial(n+k-1, n-k)*Fibonacci(k+1): k in [0..n]] : n in [0..40] ]; // Vincenzo Librandi, Nov 26 2025
CROSSREFS
Cf. A000045.
Sequence in context: A352197 A192988 A361326 * A280016 A089243 A122534
KEYWORD
sign,easy
AUTHOR
Seiichi Manyama, Nov 21 2025
STATUS
approved