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 A342527 #10 Mar 24 2021 22:19:32
%S A342527 1,1,2,4,6,8,11,12,16,17,21,20,29,24,31,32,38,32,46,36,51,46,51,44,69,
%T A342527 51,61,60,73,56,87,60,84,74,81,76,110,72,91,88,115,80,123,84,117,112,
%U A342527 111,92,153,101,132,116,139,104,159,120,161,130,141,116,205,120,151,156,178,142,195,132,183,158
%N A342527 Number of compositions of n with alternating parts equal.
%C A342527 These are finite sequences q of positive integers summing to n such that q(i) = q(i+2) for all possible i.
%H A342527 Gus Wiseman, <a href="/A069916/a069916.txt">Sequences counting and ranking partitions and compositions by their differences and quotients</a>.
%F A342527 a(n) = 1 + n + A000203(n) - 2*A000005(n).
%F A342527 a(n) = A065608(n) + A062968(n).
%e A342527 The a(1) = 1 through a(8) = 16 compositions:
%e A342527 (1) (2) (3) (4) (5) (6) (7) (8)
%e A342527 (11) (12) (13) (14) (15) (16) (17)
%e A342527 (21) (22) (23) (24) (25) (26)
%e A342527 (111) (31) (32) (33) (34) (35)
%e A342527 (121) (41) (42) (43) (44)
%e A342527 (1111) (131) (51) (52) (53)
%e A342527 (212) (141) (61) (62)
%e A342527 (11111) (222) (151) (71)
%e A342527 (1212) (232) (161)
%e A342527 (2121) (313) (242)
%e A342527 (111111) (12121) (323)
%e A342527 (1111111) (1313)
%e A342527 (2222)
%e A342527 (3131)
%e A342527 (21212)
%e A342527 (11111111)
%t A342527 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],SameQ@@Plus@@@Reverse/@Partition[#,2,1]&]],{n,0,15}]
%Y A342527 The odd-length case is A062968.
%Y A342527 The even-length case is A065608.
%Y A342527 The version with alternating parts unequal is A224958 (unordered: A000726).
%Y A342527 The version with alternating parts weakly decreasing is A342528.
%Y A342527 A000005 counts constant compositions.
%Y A342527 A000041 counts weakly increasing (or weakly decreasing) compositions.
%Y A342527 A000203 adds up divisors.
%Y A342527 A002843 counts compositions with all adjacent parts x <= 2y.
%Y A342527 A003242 counts anti-run compositions.
%Y A342527 A175342 counts compositions with constant differences.
%Y A342527 A342495 counts compositions with constant first quotients.
%Y A342527 A342496 counts partitions with constant first quotients (strict: A342515, ranking: A342522).
%Y A342527 Cf. A001522, A008965, A048004, A059966, A064410, A064428, A069916, A114921, A167606, A325545, A325557.
%K A342527 nonn
%O A342527 0,3
%A A342527 _Gus Wiseman_, Mar 24 2021