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A087018 Row sums of Fibonacci triangle shown below. 0
1, 3, 16, 123, 1453, 27060, 803383, 38256129, 2932126904, 362464081089, 72358024951979, 23344004888219544, 12176743686773409053, 10272520597198595537175, 14018081932741301581509848 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..15.

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

Cf. A000045.

Cf. A000217.

Sequence in context: A053588 A035352 A159607 * A005119 A190291 A090135

Adjacent sequences:  A087015 A087016 A087017 * A087019 A087020 A087021

KEYWORD

nonn,easy

AUTHOR

Gary Adamson, Oct 18 2003

EXTENSIONS

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

STATUS

approved

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Last modified December 22 16:00 EST 2014. Contains 252364 sequences.