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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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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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 (amnalexander(AT)yahoo.com), 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 (jvospost3(AT)gmail.com), Dec 17 2006
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EXAMPLE
| 1
1 2
3 5 8
13 21 34 55
89 144 233 377 610
...
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MATHEMATICA
| 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
| Cf. A000045.
Cf. A000217.
Sequence in context: A053588 A035352 A159607 * A005119 A190291 A090135
Adjacent sequences: A087015 A087016 A087017 * A087019 A087020 A087021
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Gary Adamson, Oct 18 2003
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 19 2003
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