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 A063686 Triangular array: a(n,k) is the number of binary necklaces (no turning over) of length n whose longest run of 1's has length k. Table begins at n=0, k=0. 1
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 4, 4, 2, 1, 1, 1, 1, 4, 6, 4, 2, 1, 1, 1, 1, 7, 11, 8, 4, 2, 1, 1, 1, 1, 9, 19, 14, 8, 4, 2, 1, 1, 1, 1, 14, 33, 27, 16, 8, 4, 2, 1, 1, 1, 1, 18, 56, 50, 30, 16, 8, 4, 2, 1, 1, 1, 1, 30, 101, 96, 59, 32, 16, 8, 4, 2, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 COMMENTS Column k=1 appears to be A032190(n), n=2,3,... LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1274 EXAMPLE Triangle begins: 1; 1, 1; 1, 1, 1; 1, 1, 1, 1; 1, 2, 1, 1, 1; 1, 2, 2, 1, 1, 1; 1, 4, 4, 2, 1, 1, 1; 1, 4, 6, 4, 2, 1, 1, 1; 1, 7, 11, 8, 4, 2, 1, 1, 1; 1, 9, 19, 14, 8, 4, 2, 1, 1, 1; 1, 14, 33, 27, 16, 8, 4, 2, 1, 1, 1; ... PROG (PARI) \\ here R(n) is A048887 transposed R(n)={Mat(vector(n, k, Col((1-x)/(1-2*x+x^(k+1)) - 1 + O(x*x^n))))} S(M)={matrix(#M-1, #M-1, n, k, if(k

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Last modified November 29 08:33 EST 2020. Contains 338762 sequences. (Running on oeis4.)