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 A325553 #8 Jan 28 2024 16:02:13
%S A325553 1,1,1,1,1,1,1,7,21,31,41,87,99,191,245,381,501,735,883,1309,1841,
%T A325553 2589,3435,4941,6857,9791,13503,19475,27073,37175,52299,72249,100359,
%U A325553 139317,190549,256769,355193,471963,644433,858793,1159161,1530879,2056073,2711921
%N A325553 Number of compositions of n with distinct circular differences up to sign.
%C A325553 A composition of n is a finite sequence of positive integers summing to n.
%C A325553 The circular differences of a composition c of length k are c_{i + 1} - c_i for i < k and c_1 - c_i for i = k. For example, the circular differences of (1,2,1,3) are (1,-1,2,-2).
%H A325553 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325553 The a(1) = 1 through a(8) = 21 compositions:
%e A325553 (1) (2) (3) (4) (5) (6) (7) (8)
%e A325553 (124) (125)
%e A325553 (142) (134)
%e A325553 (214) (143)
%e A325553 (241) (152)
%e A325553 (412) (215)
%e A325553 (421) (251)
%e A325553 (314)
%e A325553 (341)
%e A325553 (413)
%e A325553 (431)
%e A325553 (512)
%e A325553 (521)
%e A325553 (1124)
%e A325553 (1142)
%e A325553 (1241)
%e A325553 (1421)
%e A325553 (2114)
%e A325553 (2411)
%e A325553 (4112)
%e A325553 (4211)
%t A325553 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@Abs[Differences[Append[#,First[#]]]]&]],{n,20}]
%Y A325553 Cf. A000079, A008965, A167606, A173258, A325324, A325349, A325545, A325549, A325551, A325552, A325553, A325556, A325558.
%K A325553 nonn
%O A325553 0,8
%A A325553 _Gus Wiseman_, May 11 2019
%E A325553 a(0) and a(26)-a(43) from _Alois P. Heinz_, Jan 28 2024