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A117502
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Triangle, row sums = A001595.
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2
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1, 1, 2, 1, 1, 3, 1, 1, 2, 5, 1, 1, 2, 3, 8, 1, 1, 2, 3, 5, 13, 1, 1, 2, 3, 5, 8, 21, 1, 1, 2, 3, 5, 8, 13, 34, 1, 1, 2, 3, 5, 8, 13, 21, 55, 1, 1, 2, 3, 5, 8, 13, 21, 34, 89, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 144, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 233
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OFFSET
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1,3
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COMMENTS
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Row sums = A001595 = (1, 3, 9, 15, 25, 41, ...).
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LINKS
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FORMULA
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n-th row = first n Fibonacci terms, with a deletion of F(n).
Columns of the triangle are difference terms of the array in A117501.
T(n,k) = Fibonacci(k) for k < n and T(n,n) = Fibonacci(n+1). - G. C. Greubel, Jul 10 2019
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EXAMPLE
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Row 5 of the triangle = (1, 1, 2, 3, 8); the first 5 Fibonacci terms with a deletion of F(5) = 5.
First few rows of the triangle are:
1;
1, 2;
1, 1, 3;
1, 1, 2, 5;
1, 1, 2, 3, 8; ...
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MATHEMATICA
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Table[If[k==n, Fibonacci[n+1], Fibonacci[k]], {n, 20}, {k, n}]//Flatten (* G. C. Greubel, Jul 10 2019 *)
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PROG
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(PARI) T(n, k) = if(k==n, fibonacci(n+1), fibonacci(k)); \\ G. C. Greubel, Jul 10 2019
(Magma) [k eq n select Fibonacci(n+1) else Fibonacci(k): k in [1..n], n in [1..20]]; // G. C. Greubel, Jul 10 2019
(Sage)
def T(n, k):
if (k==n): return fibonacci(n+1)
else: return fibonacci(k)
[[T(n, k) for k in (1..n)] for n in (1..20)] # G. C. Greubel, Jul 10 2019
(GAP)
T:= function(n, k)
if k=n then return Fibonacci(n+1);
else return Fibonacci(k);
fi;
end;
Flat(List([1..20], n-> List([1..n], k-> T(n, k) ))); # G. C. Greubel, Jul 14 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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