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A385733
Triangle read by rows: the denominators of the Lucas triangle.
3
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 2, 14, 2, 3, 1, 1, 1, 1, 3, 3, 7, 7, 3, 3, 1, 1, 1, 1, 1, 1, 7, 77, 7, 1, 1, 1, 1, 1, 1, 1, 1, 7, 77, 77, 7, 1, 1, 1, 1, 1, 1, 3, 2, 1, 11, 99, 11, 1, 2, 3, 1, 1
OFFSET
0,13
LINKS
Diana L. Wells, The Fibonacci and Lucas triangles modulo 2, Fibonacci Quart. 32, no. 2 (1994), p. 112.
FORMULA
LT(n, k) = Product_{j=k+1..n} i^j*cosh(c*j) / Product_{j=1..n-k} i^j*cosh(c*j) where c = arccsch(2) - i*Pi/2 and i is the imaginary unit.
T(n, k) = denominator(LT(n, k)).
EXAMPLE
Triangle begins:
[0] 1;
[1] 1, 1;
[2] 1, 1, 1;
[3] 1, 1, 1, 1;
[4] 1, 1, 3, 1, 1;
[5] 1, 1, 3, 3, 1, 1;
[6] 1, 1, 1, 2, 1, 1, 1;
[7] 1, 1, 1, 2, 2, 1, 1, 1;
[8] 1, 1, 3, 2, 14, 2, 3, 1, 1;
[9] 1, 1, 3, 3, 7, 7, 3, 3, 1, 1;
MAPLE
c := arccsch(2) - I*Pi/2:
LT := (n, k) -> mul(I^j*cosh(c*j), j = k + 1..n) / mul(I^j*cosh(c*j), j = 1..n - k):
T := (n, k) -> denom(simplify(LT(n, k))): seq(seq(T(n, k), k = 0..n), n = 0..12);
MATHEMATICA
T[n_, k_] := With[{c = ArcCsch[2] - I Pi/2}, Product[I^j Cosh[c j], {j, k + 1, n}] / Product[I^j Cosh[c j], {j, 1, n - k}]];
Table[Simplify[T[n, k]], {n, 0, 8}, {k, 0, n}] // Flatten // Denominator
CROSSREFS
Cf. A385732 (numerators), A070825 (Lucanorial), A003266 (Fibonorial), A010048 (Fibonomial).
Sequence in context: A214268 A214249 A271714 * A049639 A046555 A379484
KEYWORD
nonn,tabl,frac
AUTHOR
Peter Luschny, Jul 08 2025
STATUS
approved