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 A327991 The complementary Fibonacci codes. Irregular triangle T(n, k) with n >= 0 and 0 <= k < A000045(n+1). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The complementary Fibonacci codes are binary strings enumerated in an irregular triangle CF(n, k). The first few are shown below in the Example section. The complementary Fibonacci codes are the bitwise complements of the Fibonacci codes described in A327990, in ascending order. The complementary Fibonacci codes are represented here through     T(n, k) = Product_{j=0..m} p(j)^c(j), where p(j) is the j-th prime number, c = CF(n, k) and m = length(CF(n, k)). LINKS EXAMPLE 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] PROG (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)) CROSSREFS The diagonal is A002110 (primorial numbers). Cf. A309896, A327990, A000045, A001924. Sequence in context: A068555 A167556 A221438 * A193322 A165460 A242649 Adjacent sequences:  A327988 A327989 A327990 * A327992 A327993 A327994 KEYWORD nonn,tabf AUTHOR Peter Luschny, Oct 09 2019 STATUS approved

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Last modified August 8 06:27 EDT 2020. Contains 336290 sequences. (Running on oeis4.)