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 A335649 #17 Jul 06 2020 06:00:41
%S A335649 0,10,200,3040,43320,607050,8468880,118007680,1643826800,22896269770,
%T A335649 318906570840,4441805503200,61866406977960,861688028423050,
%U A335649 12001766499380000,167163044860403200,2328280868627854560,32428769142358413450,451674487223023755240,6291014052348080593120
%N A335649 a(n) is the frequency of multi-pairs in a sequence of multi-set designs with 2 blocks.
%D A335649 A. Assaf, A. Hartman, E. Mendelsohn, Multi-set Designs-Designs having blocks with repeated elements, Congressus Numerantium, 48 (1985), 7-24.
%H A335649 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (19,-76,76,-19,1).
%F A335649 a(n) = (1/12)*((2+sqrt(3))^(2*n) + (2-sqrt(3))^(2*n) - 6*(2+sqrt(3))^n - 6*(2-sqrt(3))^n + 10).
%F A335649 a(n) = (1/3)*(A092184(n+1)*(A092184(n+1)-1)).
%F A335649 From _Colin Barker_, Jun 16 2020: (Start)
%F A335649 G.f.: 10*x^2*(1 + x) / ((1 - x)*(1 - 14*x + x^2)*(1 - 4*x + x^2)).
%F A335649 a(n) = 19*a(n-1) - 76*a(n-2) + 76*a(n-3) - 19*a(n-4) + a(n-5) for n>5.
%F A335649 (End)
%e A335649 For V={x,y} the design for n=2 are the blocks {xxxxxy,xyyyyy}. Pair frequencies of the multi-pairs xx, yy, and xy in these 2 blocks are all a(2)=10.
%e A335649 A092184(3)=6, and the above example has blocks of size 6.
%t A335649 LinearRecurrence[{19, -76, 76, -19, 1}, {0, 10, 200, 3040, 43320, 607050}, 20] (* _Amiram Eldar_, Jun 16 2020 *)
%o A335649 (PARI) concat(0, Vec(10*x^2*(1 + x) / ((1 - x)*(1 - 14*x + x^2)*(1 - 4*x + x^2)) + O(x^20))) \\ _Colin Barker_, Jun 16 2020
%Y A335649 A092184(n+1) is the block size of the n-th design in the sequence.
%K A335649 nonn,easy
%O A335649 1,2
%A A335649 _John P. McSorley_, Jun 15 2020
%E A335649 More terms from _Jinyuan Wang_, Jun 15 2020