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 A357644 #10 Oct 19 2022 18:18:06
%S A357644 1,1,1,3,4,7,8,13,17,25,30,44,58,77,98,142,176,245,311,426,548,758,
%T A357644 952,1319,1682,2308,2934,4059,5132,7087,9008,12395,15757,21728,27552,
%U A357644 38019,48272,66515,84462,116467,147812,203825,258772,356686,452876,624399,792578
%N A357644 Number of integer compositions of n into parts that are alternately unequal and equal.
%H A357644 Alois P. Heinz, <a href="/A357644/b357644.txt">Table of n, a(n) for n = 0..1000</a>
%e A357644 The a(1) = 1 through a(7) = 13 compositions:
%e A357644 (1) (2) (3) (4) (5) (6) (7)
%e A357644 (12) (13) (14) (15) (16)
%e A357644 (21) (31) (23) (24) (25)
%e A357644 (211) (32) (42) (34)
%e A357644 (41) (51) (43)
%e A357644 (122) (411) (52)
%e A357644 (311) (1221) (61)
%e A357644 (2112) (133)
%e A357644 (322)
%e A357644 (511)
%e A357644 (2113)
%e A357644 (3112)
%e A357644 (12211)
%t A357644 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],And@@Table[#[[i]]==#[[i+1]],{i,2,Length[#]-1,2}]&&And@@Table[#[[i]]!=#[[i+1]],{i,1,Length[#]-1,2}]&]],{n,0,10}]
%Y A357644 Without equal relations we have A000213, equal only A027383.
%Y A357644 Even-length opposite: A003242, ranked by A351010, partitions A035457.
%Y A357644 The version for partitions is A351006.
%Y A357644 The opposite version is A357643, partitions A351005.
%Y A357644 A011782 counts compositions.
%Y A357644 A357621 gives half-alternating sum of standard compositions, skew A357623.
%Y A357644 A357645 counts compositions by half-alternating sum, skew A357646.
%Y A357644 Cf. A001590, A029862, A035544, A097805, A122129, A122134, A122135, A351003, A351004, A351007, A357136, A357641.
%K A357644 nonn
%O A357644 0,4
%A A357644 _Gus Wiseman_, Oct 14 2022
%E A357644 More terms from _Alois P. Heinz_, Oct 19 2022