

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
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..94.


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 (* JeanFrançois 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: A334431 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



