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A087018
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Row sums of Fibonacci triangle shown below.
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0
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1, 3, 16, 123, 1453, 27060, 803383, 38256129, 2932126904, 362464081089, 72358024951979, 23344004888219544, 12176743686773409053, 10272520597198595537175, 14018081932741301581509848
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OFFSET
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1,2
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REFERENCES
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Thomas Koshy, "Elementary Number Theory with Applications", p. 143.
T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, 2001, see p. 16.
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LINKS
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FORMULA
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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
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EXAMPLE
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1
1 2
3 5 8
13 21 34 55
89 144 233 377 610
...
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MATHEMATICA
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Table[Plus@@Fibonacci[Range[((n - 1)^2 + n - 1)/2 + 1, (n^2 + n)/2]], {n, 15}] (* Alonso del Arte, Feb 10 2012 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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