OFFSET
1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
C. A. Church, Jr., Lattice paths and Fibonacci and Lucas numbers, Fibonacci Quarterly 12(4) (1974) 336-338.
W. Dotson, F. Norwood and C. Taylor, Fiber optics and Fibonacci, Math. Mag., 66 (1993), 167-174.
Index entries for linear recurrences with constant coefficients, signature (4, -4, -2, 4, 0, -1).
FORMULA
a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6). G.f.: -x*(-1+x+x^2-x^3-x^4+2*x^5)/ ((x-1)^2 * (x^2+x-1)^2). [R. J. Mathar, Feb 06 2010]
MAPLE
with(combinat): A007574 := proc(n) local k; if n=1 then RETURN(1) fi; if n=2 then RETURN(3) fi; if n=3 then RETURN(7) fi; if n>3 then RETURN( fibonacci(n)+2*fibonacci(n-1)+n*sum(fibonacci(n-k), k=2..n-1)) fi; end;
MATHEMATICA
Table[ Fibonacci[n] + 2 Fibonacci[n - 1] + n*Sum[Fibonacci[n - k], {k, 2, n - 1}], {n, 1, 35} ]
LinearRecurrence[{4, -4, -2, 4, 0, -1}, {1, 3, 7, 15, 31, 60}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2012 *)
CoefficientList[Series[-(- 1 + x + x^2 - x^3 - x^4 + 2 x^5) / ((x - 1)^2 (x^2 + x - 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 09 2013 *)
PROG
(Magma) I:=[1, 3, 7, 15, 31, 60]; [n le 6 select I[n] else 4*Self(n-1)-4*Self(n-2)-2*Self(n-3)+4*Self(n-4)-Self(n-6): n in [1..50]]; // Vincenzo Librandi, Jun 09 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved