OFFSET
0,3
COMMENTS
Hankel transform of A167422.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1).
FORMULA
G.f.: ( 1-7*x+6*x^2-x^3 ) / (x^2-3*x+1)^2 .
a(n) = F(2*n)*(1-3*n)/2 + L(2*n)*(1-n)/2. - Paul Barry, Feb 22 2010
a(n) = 1 - Sum_{k=1..n} k*F(2*k+1), where F(n) = A000045(n). - Vladimir Reshetnikov, Oct 28 2015
MATHEMATICA
Table[((1-3n) Fibonacci[2n] + (1-n) LucasL[2n])/2, {n, 0, 20}] (* Vladimir Reshetnikov, Oct 28 2015 *)
LinearRecurrence[{6, -11, 6, -1}, {1, -1, -11, -50}, 50] (* G. C. Greubel, Jun 12 2016 *)
PROG
(PARI) Vec((1-7*x+6*x^2-x^3)/(1-6*x+11*x^2-6*x^3+x^4) + O(x^100)) \\ Altug Alkan, Oct 29 2015
(Magma) [Fibonacci(2*n)*(1-3*n)/2 + Lucas(2*n)*(1-n)/2: n in [0..30]]; // Vincenzo Librandi, Jun 13 2016
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Nov 03 2009
STATUS
approved