A087018 Row sums of Fibonacci triangle shown below.

1, 3, 16, 123, 1453, 27060, 803383, 38256129, 2932126904, 362464081089, 72358024951979, 23344004888219544, 12176743686773409053, 10272520597198595537175, 14018081932741301581509848

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.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..97

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 *)
With[{nn=15}, Total/@TakeList[Fibonacci[Range[(nn(nn+1))/2]], Range[nn]]] (* Harvey P. Dale, Aug 26 2025 *)

Crossrefs

Cf. A000045.

Cf. A000217.

Sequence in context: A035352 A383170 A159607 * A005119 A190291 A090135

Adjacent sequences: A087015 A087016 A087017 * A087019 A087020 A087021

Keyword

nonn,easy

Author

Gary W. Adamson, Oct 18 2003

Extensions

More terms from Benoit Cloitre and Ray Chandler, Oct 19 2003

Status

approved