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 A008652 #43 Sep 08 2022 08:44:36 %S A008652 1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,6,6,6,6,8,8,8,8,10,10,10,10,12,12,12, %T A008652 12,15,15,15,15,18,18,18,18,21,21,21,21,24,24,24,24,28,28,28,28,32,32, %U A008652 32,32,36,36,36,36,40,40 %N A008652 Molien series for group of 3 X 3 upper triangular matrices over GF( 4 ). %C A008652 Partitions into parts 1, 4, and 16. - _Joerg Arndt_, Apr 29 2014 %D A008652 D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105. %H A008652 Vincenzo Librandi, <a href="/A008652/b008652.txt">Table of n, a(n) for n = 0..1000</a> %H A008652 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=220">Encyclopedia of Combinatorial Structures 220</a> %H A008652 <a href="/index/Mo#Molien">Index entries for Molien series</a> %H A008652 <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1). %F A008652 G.f.: 1/((1-x)*(1-x^4)*(1-x^16)). %F A008652 G.f.: 1/((1+x)^2*(1-x)^3*(1+x^2)^2*(1+x^4)*(1+x^8)). - _Bruno Berselli_, Jul 25 2013 %F A008652 a(n) ~ 1/128*n^2. - _Ralf Stephan_, Apr 29 2014 %p A008652 seq(coeff(series(1/((1-x)*(1-x^4)*(1-x^16)), x, n+1), x, n), n = 0..65); # _G. C. Greubel_, Sep 07 2019 %t A008652 Table[Floor[(Floor[n/4] + 3)^2/8], {n, 0, 61}] (* or *) Table[Floor[(n + 3)^2/8], {n, 0, 15}, {4}] // Flatten (* _Jean-François Alcover_, Jul 17 2013, updated Feb 26 2016 *) %t A008652 LinearRecurrence[{1,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1}, {1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,6,6,6,6,8}, 70] (* _Harvey P. Dale_, Jan 30 2018 *) %o A008652 (PARI) a(n)=(n\4 + 3)^2\8 \\ _Charles R Greathouse IV_, Feb 10 2017 %o A008652 (Magma) [Floor((Floor(n/4)+3)^2/8): n in [0..65]]; // _G. C. Greubel_, Sep 07 2019 %o A008652 (Sage) [floor((floor(n/4)+3)^2/8) for n in (0..65)] # _G. C. Greubel_, Sep 07 2019 %o A008652 (GAP) List([0..65], n-> Int((Int(n/4)+3)^2/8) ); # _G. C. Greubel_, Sep 07 2019~ %K A008652 nonn,easy,nice %O A008652 0,5 %A A008652 _N. J. A. Sloane_