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A104765
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Triangle T(n,k) read by rows: row n contains the first n Lucas numbers A000204.
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5
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1, 1, 3, 1, 3, 4, 1, 3, 4, 7, 1, 3, 4, 7, 11, 1, 3, 4, 7, 11, 18, 1, 3, 4, 7, 11, 18, 29, 1, 3, 4, 7, 11, 18, 29, 47, 1, 3, 4, 7, 11, 18, 29, 47, 76, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 1, 3, 4, 7, 11
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OFFSET
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1,3
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COMMENTS
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Reading rows from the right to the left yields A104764.
Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A. Sequence A104765 is the reluctant sequence of A000204. - Boris Putievskiy, Dec 14 2012
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LINKS
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FORMULA
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EXAMPLE
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First few rows of the triangle are:
1;
1, 3;
1, 3, 4;
1, 3, 4, 7;
1, 3, 4, 7, 11;
1, 3, 4, 7, 11, 18;
...
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MATHEMATICA
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Table[LucasL[k], {n, 1, 10}, {k, 1, n}] // Flatten (* G. C. Greubel, Dec 21 2017 *)
Module[{nn=20, luc}, luc=LucasL[Range[nn]]; Table[Take[luc, n], {n, nn}]]//Flatten (* Harvey P. Dale, Jul 10 2024 *)
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PROG
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(PARI) for(n=1, 10, for(k=1, n, print1(fibonacci(k+1) + fibonacci(k-1), ", "))) \\ G. C. Greubel, Dec 21 2017
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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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