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).

1, 1, 3, 4, 8, 10, 17, 20, 30, 35, 49, 56, 75, 84, 108, 120, 150, 165, 202, 220, 264, 286, 338, 364, 425, 455, 525, 560, 640, 680, 771, 816, 918, 969, 1083, 1140, 1267, 1330, 1470, 1540, 1694, 1771, 1940, 2024, 2208, 2300, 2500, 2600, 2817, 2925, 3159, 3276, 3528, 3654, 3925

Offset: 0

Author

Alexander Karpov, Apr 12 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• A. Karpov, An Informational Basis for Voting Rules, NRU Higher School of Economics. Series WP BRP "Economics/EC". 2018. No. 188
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1,1,-1,-2,2,1,-1).

Crossrefs

Cf. A037240, A005513.

For odd n, it is A000292.

Programs

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

Formula

a(n) = 2*A005513(n-6) - A037240(n).

If n is odd, a(n) = (n+5)*(n+3)*(n+1)/48;

If n is even, a(n) = ceiling((n+4)^2*(n+2)/48).

From Colin Barker, May 11 2018: (Start)

G.f.: (1 + x^3 + x^4) / ((1 - x)^4*(1 + x)^3*(1 - x + x^2)*(1 + x + x^2)).

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.

(End)