OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-11,17,-14,6,-1).
FORMULA
G.f.: 1/((1-x)^6 * (1+g-g^2)), where g = x/(1-x)^3.
G.f.: 1 / ((1 - 3*x + x^2) * (1 - 2*x + 4*x^2 - 3*x^3 + x^4)).
a(n) = 5*a(n-1) - 11*a(n-2) + 17*a(n-3) - 14*a(n-4) + 6*a(n-5) - a(n-6).
MATHEMATICA
Table[Sum[(-1)^k*Binomial[n+2*k+5, 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+2*k+5, n-k)*fibonacci(k+1));
(Magma) [&+[(-1)^k*Binomial(n+2*k+5, n-k)*Fibonacci(k+1): k in [0..n]] : n in [0..40] ]; // Vincenzo Librandi, Nov 26 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Nov 21 2025
STATUS
approved
