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A294085 a(n) is the number of self-symmetric anonymous and neutral equivalence classes of preference profiles with 3 alternatives and n agents (IANC model).

%I A294085 #34 May 20 2018 13:54:12
%S A294085 1,1,3,4,8,10,17,20,30,35,49,56,75,84,108,120,150,165,202,220,264,286,
%T A294085 338,364,425,455,525,560,640,680,771,816,918,969,1083,1140,1267,1330,
%U A294085 1470,1540,1694,1771,1940,2024,2208,2300,2500,2600,2817,2925,3159,3276,3528,3654,3925
%N A294085 a(n) is the number of self-symmetric anonymous and neutral equivalence classes of preference profiles with 3 alternatives and n agents (IANC model).
%H A294085 Colin Barker, <a href="/A294085/b294085.txt">Table of n, a(n) for n = 0..1000</a>
%H A294085 A. Karpov, <a href="https://publications.hse.ru/mirror/pubs/share//direct/217868605">An Informational Basis for Voting Rules</a>, NRU Higher School of Economics. Series WP BRP "Economics/EC". 2018. No. 188
%H A294085 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1,1,-1,-2,2,1,-1).
%F A294085 a(n) = 2*A005513(n-6) - A037240(n).
%F A294085 If n is odd, a(n) = (n+5)*(n+3)*(n+1)/48;
%F A294085 If n is even, a(n) = ceiling((n+4)^2*(n+2)/48).
%F A294085 From _Colin Barker_, May 11 2018: (Start)
%F A294085 G.f.: (1 + x^3 + x^4) / ((1 - x)^4*(1 + x)^3*(1 - x + x^2)*(1 + x + x^2)).
%F A294085 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) + a(n-6) - a(n-7) - 2*a(n-8) + 2*a(n-9) + a(n-10) - a(n-11) for n>10.
%F A294085 (End)
%o A294085 (PARI) Vec((1 + x^3 + x^4) / ((1 - x)^4*(1 + x)^3*(1 - x + x^2)*(1 + x + x^2)) + O(x^60)) \\ _Colin Barker_, May 11 2018
%Y A294085 Cf. A037240, A005513.
%Y A294085 For odd n, it is A000292.
%K A294085 nonn,easy
%O A294085 0,3
%A A294085 _Alexander Karpov_, Apr 12 2018