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A158753
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Triangle T(n, k) = A000032(2*(n-k) + 1), read by rows.
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2
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1, 4, 1, 11, 4, 1, 29, 11, 4, 1, 76, 29, 11, 4, 1, 199, 76, 29, 11, 4, 1, 521, 199, 76, 29, 11, 4, 1, 1364, 521, 199, 76, 29, 11, 4, 1, 3571, 1364, 521, 199, 76, 29, 11, 4, 1, 9349, 3571, 1364, 521, 199, 76, 29, 11, 4, 1, 24476, 9349, 3571, 1364, 521, 199, 76, 29, 11, 4, 1
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text;
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OFFSET
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2,2
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REFERENCES
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H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, pp. 159-162.
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LINKS
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FORMULA
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T(n, k) = 5*e(n, k), where e(n,k) = (e(n-1, k)*e(n, k-1) + 1)/e(n-1, k-1), and e(n, 0) = GoldenRatio^(n) + GoldenRatio^(-n).
Sum_{k=0..n} T(n, k) = A004146(n-1).
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EXAMPLE
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Triangle begins as:
1;
4, 1;
11, 4, 1;
29, 11, 4, 1;
76, 29, 11, 4, 1;
199, 76, 29, 11, 4, 1;
521, 199, 76, 29, 11, 4, 1;
1364, 521, 199, 76, 29, 11, 4, 1;
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MATHEMATICA
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Table[LucasL[2*(n-k) + 1], {n, 2, 16}, {k, 2, n}]//Flatten (* G. C. Greubel, Dec 06 2021 *)
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PROG
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(Magma) [Lucas(2*n-2*k+1): k in [2..n], n in [2..16]]; // G. C. Greubel, Dec 06 2021
(Sage) flatten([[lucas_number2(2*(n-k)+1, 1, -1) for k in (2..n)] for n in (2..16)]) # G. C. Greubel, Dec 06 2021
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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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