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

0,3

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).

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)

Prog

(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

Crossrefs

Cf. A037240, A005513.

For odd n, it is A000292.

Sequence in context: A005232 A165272 A310010 * A115264 A210631 A212543

Adjacent sequences: A294082 A294083 A294084 * A294086 A294087 A294088

Keyword

nonn,easy

Author

Alexander Karpov, Apr 12 2018

Status

approved