OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Prabha Sivaraman Nair and Rejikumar Karunakaran, On k-Fibonacci Brousseau Sums, J. Int. Seq. (2024) Art. No. 24.6.4. See p. 2.
Index entries for linear recurrences with constant coefficients, signature (4,-2,-8,5,8,-2,-4,-1).
FORMULA
G.f.: x*(x^2+1)*(x^4-4*x^3+23*x^2+4*x+1) / (x^2+x-1)^4.
Sum_{k=1..n} a(k) = (n^3-6*n^2+24*n-50)*A000045(n+1) + ((n+1)^3-6*(n+1)^2+24*(n+1)-50)*A000045(n) + 50. - Prabha Sivaramannair, Jul 15 2024
E.g.f.: exp(x/2)*x*(5*(1 + x)*(1 + 2*x)*cosh(sqrt(5)*x/2) + sqrt(5)*(1 + x*(9 + 4*x))*sinh(sqrt(5)*x/2))/5. - Stefano Spezia, Aug 25 2024
MAPLE
a:= n-> n^3*(<<1|1>, <1|0>>^n)[1, 2]:
seq(a(n), n=0..50); # Alois P. Heinz, Jun 30 2015
MATHEMATICA
Array[#^3*Fibonacci[#] &, 50, 0] (* Paolo Xausa, Jul 15 2024 *)
PROG
(PARI) a(n) = n^3*fibonacci(n)
(PARI) concat(0, Vec(x*(x^2+1)*(x^4-4*x^3+23*x^2+4*x+1)/(x^2+x-1)^4 + O(x^50)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jun 30 2015
STATUS
approved