A259451 a(n) = n^2*Fibonacci(n).
0, 1, 4, 18, 48, 125, 288, 637, 1344, 2754, 5500, 10769, 20736, 39377, 73892, 137250, 252672, 461533, 837216, 1509341, 2706000, 4827186, 8572124, 15159553, 26707968, 46890625, 82061668, 143188722, 249163824, 432466589, 748836000, 1293764509, 2230588416, 3838265442, 6592537372, 11303644625, 19349736192
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,0,-5,0,3,1).
Programs
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Maple
a:= n-> n^2*(<<1|1>, <1|0>>^n)[1, 2]: seq(a(n), n=0..50); # Alois P. Heinz, Jun 30 2015
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Mathematica
a[n_] := n^2 MatrixPower[{{1, 1}, {1, 0}}, n][[1, 2]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 14 2016, after Alois P. Heinz *) -
PARI
concat(0, Vec(-x*(x^4-x^3+6*x^2+x+1)/(x^2+x-1)^3 + O(x^100))) \\ Colin Barker, Jun 29 2015
Formula
From Colin Barker, Jun 29 2015: (Start)
a(n) = 3*a(n-1) - 5*a(n-3) + 3*a(n-5) + a(n-6).
G.f.: -x*(x^4 - x^3 + 6*x^2 + x + 1)/(x^2 + x - 1)^3. (End)
E.g.f.: exp(x/2)*x*(sqrt(5)*(1 + x)*cosh(sqrt(5)*x/2) + (1 + 3*x)*sinh(sqrt(5)*x/2))/sqrt(5). - Stefano Spezia, Mar 04 2023