A327991 The complementary Fibonacci codes. Irregular triangle T(n, k) with n >= 0 and 0 <= k < A000045(n+1).
1, 2, 2, 6, 2, 6, 30, 2, 6, 30, 10, 210, 2, 6, 30, 10, 210, 42, 70, 2310, 2, 6, 30, 10, 210, 42, 70, 2310, 14, 330, 462, 770, 30030, 2, 6, 30, 10, 210, 42, 70, 2310, 14, 330, 462, 770, 30030, 66, 110, 2730, 154, 4290, 6006, 10010, 510510
Offset: 0
Examples
The complementary Fibonacci codes start: [0] [[]] [1] [[1]] [2] [[1][11]] [3] [[1][11][111]] [4] [[1][11][111][101][1111]] [5] [[1][11][111][101][1111][1101][1011][11111]] [6] [[1][11][111][101][1111][1101][1011][11111][1001][11101][11011][10111][111111]] [7] [[1][11][111][101][1111][1101][1011][11111][1001][11101][11011][10111][111111] [11001][10101][111101][10011][111011][110111][101111][1111111]] The representation of the complementary Fibonacci codes starts: [0] [1] [1] [2] [2] [2, 6] [3] [2, 6, 30] [4] [2, 6, 30, 10, 210] [5] [2, 6, 30, 10, 210, 42, 70, 2310] [6] [2, 6, 30, 10, 210, 42, 70, 2310, 14, 330, 462, 770, 30030] [7] [2, 6, 30, 10, 210, 42, 70, 2310, 14, 330, 462, 770, 30030, 66, 110, 2730, 154, 4290, 6006, 10010, 510510]
Programs
-
SageMath
@cached_function def FibonacciCodes(n): if n == 0 : return [[]] if n == 1 : return [[1]] A = [c.conjugate() for c in Compositions(n) if not(1 in c)] return FibonacciCodes(n-1) + [[2-i for i in a] for a in A] def A327991row(n): P = Primes() M = lambda C: mul(P[i]^c for (i, c) in enumerate(C)) return [M(c) for c in FibonacciCodes(n)] for n in (0..7): print(A327991row(n))
Comments