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 A165190 #27 Apr 14 2023 14:28:37
%S A165190 1,0,0,0,1,1,0,0,1,1,1,0,1,1,1,1,1,1,1,1,2,1,1,1,2,2,1,1,2,2,2,1,2,2,
%T A165190 2,2,2,2,2,2,3,2,2,2,3,3,2,2,3,3,3,2,3,3,3,3,3,3,3,3,4,3,3,3,4,4,3,3,
%U A165190 4,4,4,3,4,4,4,4,4,4,4,4,5,4,4,4,5,5,4,4,5,5,5,4,5,5,5,5,5,5,5,5,6,5,5,5,6
%N A165190 G.f.: 1/((1-x^4)*(1-x^5)).
%C A165190 A121262 convolved with A079998. The two sequences have very simple generating functions and can be mapped to the numeric partitions 4=4 and 5=5 respectively.
%C A165190 Number of partitions of n into parts 4 and 5. - _Joerg Arndt_, Aug 28 2015
%H A165190 Michael De Vlieger, <a href="/A165190/b165190.txt">Table of n, a(n) for n = 0..10000</a>
%H A165190 A. V. Kitaev and A. Vartanian, <a href="https://arxiv.org/abs/2304.05671">Algebroid Solutions of the Degenerate Third Painlevé Equation for Vanishing Formal Monodromy Parameter</a>, arXiv:2304.05671 [math.CA], 2023. See p. 20.
%H A165190 <a href="/index/Mo#Molien">Index to Molien series</a>
%H A165190 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,1,0,0,0,-1).
%F A165190 1 followed by the Euler transform of the finite sequence [0,0,0,1,1].
%F A165190 G.f.: 1/((1-x)^2*(1+x)*(1+x^2)*(1+x+x^2+x^3+x^4)). [_R. J. Mathar_, Oct 07 2009]
%F A165190 a(n) = A117444(n+2)/5 + n/20 + 9/40 + (-1)^n/8 + A057077(n)/4. [_R. J. Mathar_, Oct 07 2009]
%F A165190 a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=1, a(6)=0, a(7)=0, a(8)=1, a(n) = a(n-4)+a(n-5)-a(n-9), n>8. - _Harvey P. Dale_, Aug 16 2012
%F A165190 a(n) = floor((n+4)/4) - floor((n+4)/5). - _Wesley Ivan Hurt_, Aug 27 2015
%F A165190 a(n)+a(n-2) = A008616(n). - _R. J. Mathar_, Jun 23 2021
%p A165190 A165190:=n->floor((n+4)/4) - floor((n+4)/5): seq(A165190(n), n=0..100); # _Wesley Ivan Hurt_, Aug 27 2015
%t A165190 CoefficientList[Series[1/((1-x^4)(1-x^5)),{x,0,110}],x] (* or *) LinearRecurrence[{0,0,0,1,1,0,0,0,-1},{1,0,0,0,1,1,0,0,1},110] (* _Harvey P. Dale_, Aug 16 2012 *)
%t A165190 Table[Floor[(n + 4)/4] - Floor[(n + 4)/5], {n, 0, 100}] (* _Wesley Ivan Hurt_, Aug 27 2015 *)
%o A165190 (Magma) [Floor((n+4)/4) - Floor((n+4)/5) : n in [0..100]]; // _Wesley Ivan Hurt_, Aug 27 2015
%Y A165190 Cf. A057077, A079998, A117444, A121262.
%K A165190 nonn,easy
%O A165190 0,21
%A A165190 _Alford Arnold_, Sep 24 2009
%E A165190 Removed duplicate of comment in A165188; Euler transform formula corrected - _R. J. Mathar_, Oct 07 2009