A385734 Lucas triangle A385732/A385733 mod 2.

1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, -1, 0, 0, 1, 1, 1, 0, -1, -1, 0, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1

Offset

0

Comments

By convention T(n, k) = -1 if the modular inverse of the corresponding entry of the Lucas triangle does not exist.

Links

Table of n, a(n) for n=0..90.

Diana L. Wells, The Fibonacci and Lucas triangles modulo 2, Fibonacci Quart. 32, no. 2 (1994), p. 112.

Example

Triangle begins:
  [0] 1;
  [1] 1, 1;
  [2] 1, 1, 1;
  [3] 1, 0, 0,  1;
  [4] 1, 1, 0,  1,  1;
  [5] 1, 1, 1,  1,  1,  1;
  [6] 1, 0, 0, -1,  0,  0, 1;
  [7] 1, 1, 0, -1, -1,  0, 1, 1;
  [8] 1, 1, 1, -1, -1, -1, 1, 1, 1;
  [9] 1, 0, 0,  1,  0,  0, 1, 0, 0, 1;

Maple

Mod2 := proc(n) try modp(n, 2); catch: return -1; end try; end;
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) -> Mod2(simplify(LT(n, k))): seq(seq(T(n, k), k = 0..n), n = 0..11);

Crossrefs

Cf. A385732, A385733, A385456 (Fibonacci).

Sequence in context: A127236 A385456 A117947 * A175860 A351956 A092152

Adjacent sequences: A385731 A385732 A385733 * A385735 A385736 A385737

Keyword

sign,tabl

Author

Peter Luschny, Jul 08 2025

Status

approved