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 A325546 #18 Aug 28 2019 10:23:56
%S A325546 1,1,2,4,7,11,19,28,41,62,87,120,170,228,303,408,534,689,899,1145,
%T A325546 1449,1842,2306,2863,3571,4398,5386,6610,8039,9716,11775,14157,16938,
%U A325546 20293,24166,28643,33995,40134,47199,55540,65088,75994,88776,103328,119886,139126
%N A325546 Number of compositions of n with weakly increasing differences.
%C A325546 Also compositions of n whose plot is concave-up.
%C A325546 A composition of n is a finite sequence of positive integers summing to n.
%C A325546 The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (3,1,2) are (-2,1).
%H A325546 Andrew Howroyd, <a href="/A325546/b325546.txt">Table of n, a(n) for n = 0..1000</a>
%H A325546 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325546 The a(1) = 1 through a(6) = 19 compositions:
%e A325546 (1) (2) (3) (4) (5) (6)
%e A325546 (11) (12) (13) (14) (15)
%e A325546 (21) (22) (23) (24)
%e A325546 (111) (31) (32) (33)
%e A325546 (112) (41) (42)
%e A325546 (211) (113) (51)
%e A325546 (1111) (212) (114)
%e A325546 (311) (123)
%e A325546 (1112) (213)
%e A325546 (2111) (222)
%e A325546 (11111) (312)
%e A325546 (321)
%e A325546 (411)
%e A325546 (1113)
%e A325546 (2112)
%e A325546 (3111)
%e A325546 (11112)
%e A325546 (21111)
%e A325546 (111111)
%t A325546 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],LessEqual@@Differences[#]&]],{n,0,15}]
%o A325546 (PARI) \\ Row sums of R(n) give A007294 (=breakdown by width).
%o A325546 R(n)={my(L=List(), v=vectorv(n, i, 1), w=1, t=1); while(v, listput(L,v); w++; t+=w; v=vectorv(n, i, sum(k=1, (i-w-1)\t + 1, v[i-w-(k-1)*t]))); Mat(L)}
%o A325546 seq(n)={my(M=R(n)); Vec(1 + sum(i=1, n, my(p=sum(w=1, min(#M,n\i), x^(w*i)*sum(j=1, n-i*w, x^j*M[j,w]))); x^i/(1 - x^i)*(1 + p + O(x*x^(n-i)))^2))} \\ _Andrew Howroyd_, Aug 28 2019
%Y A325546 Cf. A000079, A000740, A007294, A008965, A070211 (concave-down compositions), A173258, A175342, A240026, A325360, A325545, A325547, A325548, A325552, A325557.
%K A325546 nonn
%O A325546 0,3
%A A325546 _Gus Wiseman_, May 10 2019
%E A325546 More terms from _Alois P. Heinz_, May 11 2019