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 A008616 #48 Sep 08 2022 08:44:36
%S A008616 1,0,1,0,1,1,1,1,1,1,2,1,2,1,2,2,2,2,2,2,3,2,3,2,3,3,3,3,3,3,4,3,4,3,
%T A008616 4,4,4,4,4,4,5,4,5,4,5,5,5,5,5,5,6,5,6,5,6,6,6,6,6,6,7,6,7,6,7,7,7,7,
%U A008616 7,7,8,7,8,7,8,8,8,8,8,8,9,8,9,8,9,9,9,9,9,9,10,9,10,9,10,10,10,10,10,10
%N A008616 Expansion of 1/((1-x^2)(1-x^5)).
%C A008616 Number of partitions of n into parts of size two and five.
%C A008616 It appears that, for n >= 2, a(n-2) is also (1) the number of partitions of 3n that are 6-term arithmetic progressions and (2) floor(n/2) - floor(2n/5). - _John W. Layman_, Jun 29 2009
%D A008616 G. E. Andrews, K. Eriksson, Integer Partitions, Cambridge Univ. Press, 2004. page 30, Exercise 48.
%D A008616 D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 100.
%H A008616 Vincenzo Librandi, <a href="/A008616/b008616.txt">Table of n, a(n) for n = 0..1000</a>
%H A008616 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=213">Encyclopedia of Combinatorial Structures 213</a>
%H A008616 M. Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Janjic/janjic63.html">On Linear Recurrence Equations Arising from Compositions of Positive Integers</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7.
%H A008616 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H A008616 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 0, 0, 1, 0, -1).
%F A008616 G.f.: 1/((1-x^2)(1-x^5)) = 1/((x-1)^2*(1+x)*(1+x+x^2+x^3+x^4)).
%F A008616 Euler transform of finite sequence [0, 1, 0, 0, 1].
%F A008616 a(n) = -a(-7 - n) = a(n - 10) + 1 = a(n - 2) + a(n - 5) - a(n - 7). - _Michael Somos_, Jan 25 2005
%F A008616 A000217(a(n)) = A025810(n). - _Michael Somos_, Dec 15 2002
%F A008616 a(n) = 7/20 + n/10 + (-1)^n/4 + (A105384(n) + 2*(A010891(n) + A105384(n+4)))/5. - _R. J. Mathar_, Jun 28 2009
%F A008616 a(n) = floor(n/10 + (3 + (-1)^n)/4). - _Tani Akinari_, Jun 20 2013
%t A008616 CoefficientList[Series[1 / ((1 - x^2) (1 - x^5)),{x, 0, 100}], x] (* _Vincenzo Librandi_, Jun 21 2013 *)
%o A008616 (PARI) {a(n) = if( n<-6, -a(-7 - n), polcoeff( 1 / (1 - x^2) / (1 - x^5) + x * O(x^n), n))} /* _Michael Somos_, Jan 25 2005 */
%o A008616 (PARI) a(n) = floor(n/10+(3+(-1)^n)/4) \\ _Charles R Greathouse IV_, Jun 19 2013
%o A008616 (Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^2)*(1-x^5)))); // _Wesley Ivan Hurt_, Dec 27 2021
%Y A008616 Cf. A000217, A025810.
%Y A008616 Cf. A008615. - _John W. Layman_, Jun 29 2009
%K A008616 nonn,easy
%O A008616 0,11
%A A008616 _N. J. A. Sloane_