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 A056951 Triangle whose rows show the result of flipping the first, first two, ... and finally first n coins when starting with the stack (1,2,3,4,...,n) [starting with all heads up, where signs show whether particular coins end up heads or tails]. 5
 -1, -2, 1, -3, -1, 2, -4, -2, 1, 3, -5, -3, -1, 2, 4, -6, -4, -2, 1, 3, 5, -7, -5, -3, -1, 2, 4, 6, -8, -6, -4, -2, 1, 3, 5, 7, -9, -7, -5, -3, -1, 2, 4, 6, 8, -10, -8, -6, -4, -2, 1, 3, 5, 7, 9, -11, -9, -7, -5, -3, -1, 2, 4, 6, 8, 10, -12, -10, -8, -6, -4, -2, 1, 3, 5, 7, 9, 11, -13, -11, -9, -7, -5, -3, -1, 2, 4, 6, 8, 10, 12, -14, -12, -10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA T(n, k) = 2k - n - b with 1 <= k <= n (where b = 2 if 2k <= n + 1, b = 1 otherwise). EXAMPLE Third row is constructed by starting from (1, 2, 3), going to (-1, 2, 3), then going to (-2, 1, 3) and finally going to (-3, -1, 2). Rows are: (-1), (-2, 1), (-3, -1, 2), (-4, -2, 1, 3) etc. as each row is reverse of previous row, with signs changed and -n added as the first term in the row. MATHEMATICA t[n_, 1] := -n; t[n_, n_] := n - 1; t[n_, k_] := 2 * k - n - If[2 * k <= n + 1, 2, 1]; Table[t[n, k], {n, 14}, {k, n}] // Flatten (* Jean-François Alcover, Oct 03 2013 *) CROSSREFS A003558 is the number of times the operation needs to be repeated to return to the starting point, taking no account of heads/tails (i.e., signs). A002326 is the number required if heads/tails (i.e., signs) are also required to return to their original position. Cf. A130517 (unsigned version). Sequence in context: A342011 A087295 A175344 * A130517 A316715 A130212 Adjacent sequences:  A056948 A056949 A056950 * A056952 A056953 A056954 KEYWORD easy,sign,tabl AUTHOR Henry Bottomley, Sep 05 2000 STATUS approved

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Last modified August 4 09:23 EDT 2021. Contains 346445 sequences. (Running on oeis4.)