OFFSET
1,2
REFERENCES
Thomas Koshy, "Elementary Number Theory with Applications", p. 143.
T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, 2001, see p. 16.
FORMULA
a(n) is asymptotic to (1/2+3/2/sqrt(5))*phi^(n*(n+1)/2) where phi=(1+sqrt(5))/2. - Benoit Cloitre, Oct 19 2003
a(n) = Sum(i=(n(n-1)/2)+1 to n(n+1)/2) fibonacci(i) - Sam Alexander, Oct 19 2003
a(n) = F(T(n)+2) - F(T(n-1)+2) where T(n) = n-th triangular number. a(n) = A000045(A000217(n)+2) - A000045(A000217(n-1)+2). - Jonathan Vos Post, Dec 17 2006
EXAMPLE
1
1 2
3 5 8
13 21 34 55
89 144 233 377 610
...
MATHEMATICA
Table[Plus@@Fibonacci[Range[((n - 1)^2 + n - 1)/2 + 1, (n^2 + n)/2]], {n, 15}] (* Alonso del Arte, Feb 10 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Oct 18 2003
EXTENSIONS
More terms from Benoit Cloitre and Ray Chandler, Oct 19 2003
STATUS
approved