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].

-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

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 (* 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