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 A077229 #22 May 12 2025 00:03:40
%S A077229 1,1,1,3,5,11,23,48,98,204,421,863,1766,3606,7341,14913,30233,61175,
%T A077229 123589,249344,502443,1011366,2033894,4086975,8206833,16469875,
%U A077229 33035611,66234372,132745859,265961487,532717894,1066778687,2135822457,4275459730,8557335141,17125445575,34268965676,68568213419,137187103849,274458924246
%N A077229 Number of compositions of n where the largest part is less than or equal to the number of parts.
%H A077229 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A077229 G.f.: 1 + Sum_{k>=0} ((x^(k+1)-x)/(x-1))^k. - _Vladeta Jovovic_, Sep 24 2004
%F A077229 G.f.: 1 + Sum_{n>=1} q^n * ( (1-q^n)/(1-q) )^n, the g.f. above, slightly rewritten. [_Joerg Arndt_, Mar 30 2014]
%F A077229 a(n) ~ 2^(n-1). - _Vaclav Kotesovec_, May 01 2014
%F A077229 a(n) = A098124(n)+A098125(n). - _R. J. Mathar_, Oct 01 2021
%e A077229 a(5)=11 since 5 can be written as 1+1+1+1+1, 1+1+1+2, 1+1+2+1, 1+1+3, 1+2+1+1, 1+2+2, 1+3+1, 2+1+1+1, 2+1+2, 2+2+1, or 3+1+1; but not as 2+3 since then the largest part (3) would be greater than the number of parts (2).
%t A077229 Table[SeriesCoefficient[1 + Sum[x^k*((1-x^k)/(1-x))^k,{k,1,n}],{x,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, May 01 2014 *)
%Y A077229 Row sums of A077227.
%Y A077229 Cf. A064174, A348125.
%K A077229 nonn
%O A077229 0,4
%A A077229 _Henry Bottomley_, Oct 29 2002
%E A077229 More terms from _Vladeta Jovovic_, Sep 24 2004
%E A077229 Prepended a(0) = 1, _Joerg Arndt_, Mar 30 2014