OFFSET
0,3
COMMENTS
Binomial transform of A093968.
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
Rigoberto Flórez, Robinson Higuita and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018.
Index entries for linear recurrences with constant coefficients, signature (4,-2,-4,-1).
FORMULA
G.f.: x*(1+x^2)/(1 - 2*x - x^2)^2;
a(n) = n*((1+sqrt(2))^n - (1-sqrt(2))^n)/(2*sqrt(2));
a(n) = n * A000129(n).
MAPLE
seq(fibonacci(n, 2)*n, n=0..27); # Zerinvary Lajos, Apr 05 2008
MATHEMATICA
LinearRecurrence[{4, -2, -4, -1}, {0, 1, 4, 15}, 30] (* Vincenzo Librandi, Dec 20 2015 *)
PROG
(PARI) { default(realprecision, 100); s=sqrt(2); for (n=0, 100, a=n*round(((1+s)^n-(1-s)^n)/(2*s)); write("b093967.txt", n, " ", a); ) } \\ Harry J. Smith, Jun 17 2009
(Magma) I:=[0, 1, 4, 15]; [n le 4 select I[n] else 4*Self(n-1)-2*Self(n-2)-4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 20 2015
(Sage) [n*lucas_number1(n, 2, -1) for n in (0..30)] # G. C. Greubel, Dec 28 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 21 2004
STATUS
approved