A357622 - OEIS

A357622

Half-alternating sum of the reversed n-th composition in standard order.

0, 1, 2, 2, 3, 3, 3, 1, 4, 4, 4, 0, 4, 2, 2, 0, 5, 5, 5, -1, 5, 1, 1, -1, 5, 3, 3, -1, 3, 1, 1, 1, 6, 6, 6, -2, 6, 0, 0, -2, 6, 2, 2, -2, 2, 0, 0, 2, 6, 4, 4, -2, 4, 0, 0, 0, 4, 2, 2, 0, 2, 2, 2, 2, 7, 7, 7, -3, 7, -1, -1, -3, 7, 1, 1, -3, 1, -1, -1, 3, 7, 3

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OFFSET

0,3

COMMENTS

We define the half-alternating sum of a sequence (A, B, C, D, E, F, G, ...) to be A + B - C - D + E + F - G - ...

The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.

LINKS

Table of n, a(n) for n=0..81.

Gus Wiseman, Statistics, classes, and transformations of standard compositions

EXAMPLE

The 357-th composition is (2,1,3,2,1) so a(357) = 1 + 2 - 3 - 1 + 2 = 1.

MATHEMATICA

stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;

halfats[f_]:=Sum[f[[i]]*(-1)^(1+Ceiling[i/2]), {i, Length[f]}];

Table[halfats[Reverse[stc[n]]], {n, 0, 100}]

CROSSREFS

See link for sequences related to standard compositions.

This is the reverse version of A357621.