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A056951
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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.].
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5
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-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; internal format)
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OFFSET
| 1,2
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FORMULA
| T(n, k) = 2k-n-b with 1<=k<=n (where b=2 if 2k<=n+1, b=1 otherwise)
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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.
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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.
Sequence in context: A087295 A175344 A130517 * A130212 A133737 A125047
Adjacent sequences: A056948 A056949 A056950 * A056952 A056953 A056954
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Sep 05 2000
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