This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A357847 #10 Oct 19 2022 19:50:05
%S A357847 1,0,0,1,0,1,3,1,8,11,15,46,59,127,259,407,888,1591,2925,5896,10607,
%T A357847 20582,39446,73448,142691,269777,513721,988638,1876107,3600313,
%U A357847 6893509,13165219,25288200,48408011,92824505,178248758,341801149,656641084,1261298356
%N A357847 Number of integer compositions of n whose length is twice their alternating sum.
%C A357847 The alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^(i-1) y_i.
%H A357847 Alois P. Heinz, <a href="/A357847/b357847.txt">Table of n, a(n) for n = 0..3465</a>
%e A357847 The a(0) = 1 through a(9) = 15 compositions:
%e A357847 () . . (21) . (32) (1131) (43) (1142) (54)
%e A357847 (2121) (1241) (111141)
%e A357847 (3111) (2132) (112131)
%e A357847 (2231) (113121)
%e A357847 (3122) (114111)
%e A357847 (3221) (211131)
%e A357847 (4112) (212121)
%e A357847 (4211) (213111)
%e A357847 (311121)
%e A357847 (312111)
%e A357847 (411111)
%t A357847 ats[y_]:=Sum[(-1)^(i-1)*y[[i]],{i,Length[y]}];
%t A357847 Table[Length[Select[Join @@ Permutations/@IntegerPartitions[n],Length[#]==2ats[#]&]],{n,0,10}]
%Y A357847 The version for partitions is A357709, ranked by A357848.
%Y A357847 A011782 counts compositions.
%Y A357847 A025047 counts alternating compositions.
%Y A357847 A103919 counts partitions by alternating sum, full triangle A344651.
%Y A357847 A357136 counts compositions by alternating sum, full triangle A097805.
%Y A357847 A357182 counts compositions w/ length = alternating sum, ranked by A357184.
%Y A357847 A357189 counts partitions w/ length = alternating sum, ranked by A357486.
%Y A357847 Cf. A262977, A301987, A357183, A357485, A357488.
%K A357847 nonn
%O A357847 0,7
%A A357847 _Gus Wiseman_, Oct 16 2022
%E A357847 a(21)-a(38) from _Alois P. Heinz_, Oct 19 2022