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A158753
Triangle T(n, k) = A000032(2*(n-k) + 1), read by rows.
2
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
OFFSET
2,2
REFERENCES
H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, pp. 159-162.
FORMULA
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).
T(n, k) = A000032(2*(n-k) + 1). - G. C. Greubel, Dec 06 2021
EXAMPLE
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;
MATHEMATICA
Table[LucasL[2*(n-k) + 1], {n, 2, 16}, {k, 2, n}]//Flatten (* G. C. Greubel, Dec 06 2021 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
EXTENSIONS
Edited by G. C. Greubel, Dec 06 2021
STATUS
approved