The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A357706 Numbers k such that the k-th composition in standard order has half-alternating sum and skew-alternating sum both 0. 2
 0, 15, 45, 54, 59, 153, 170, 179, 204, 213, 230, 235, 247, 255, 561, 594, 611, 660, 677, 710, 715, 727, 735, 750, 765, 792, 809, 842, 851, 871, 879, 894, 908, 917, 934, 939, 951, 959, 973, 982, 987, 1005, 1014, 1019 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 - ..., and the skew-alternating sum 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=1..44. FORMULA Intersection of A357625 and A357627. 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]}]; skats[f_]:=Sum[f[[i]]*(-1)^(1+Ceiling[(i+1)/2]), {i, Length[f]}]; Select[Range[0, 1000], halfats[stc[#]]==0&&skats[stc[#]]==0&] CROSSREFS For partitions and half only (or both): A000583, counted by A035363. These compositions are counted by A228248. For half-alternating only: A357625, reverse A357626, counted by A357641. For skew-alternating only: A357627, reverse A357628, counted by A001700. For reversed partitions and half only: A357631, counted by A357639. For reversed partitions and skew only A357632, counted by A357640. For partitions and skew only: A357636, counted by A035594. Cf. A001511, A004006, A088218, A357136, A357182, A357642. Sequence in context: A289669 A295980 A029827 * A119123 A293625 A084821 Adjacent sequences: A357703 A357704 A357705 * A357707 A357708 A357709 KEYWORD nonn AUTHOR Gus Wiseman, Oct 13 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 20 23:17 EDT 2024. Contains 374461 sequences. (Running on oeis4.)