A110100 a(n) is the number of 2-regular 3-hypergraphs on 3n labeled vertices. (In a 3-hypergraph, each hyper-edge is a proper 3-set; 2-regular implies that each vertex is in exactly 2 hyperedges.)

1, 0, 75, 122220, 757275750, 12713292692100, 474415445827323000, 34461884930947363890000, 4431555785100983345799993000, 939388724430508823324694340500000

Offset

0,3

Comments

P-recursive

Links

Table of n, a(n) for n=0..9.

Denis S. Krotov, Konstantin V. Vorob'ev, On unbalanced Boolean functions attaining the bound 2n/3-1 on the correlation immunity, arXiv:1812.02166 [math.CO], 2018.

Marni Mishna, Maple worksheet

Formula

Recurrence: {a(0) = 1, a(1) = 0, (361631520*n + 1358261784*n^2 + 2841968052*n^3 + 3241507005*n^5 + 3725654130*n^4 + 1922779782*n^6 + 781684101*n^7 + 214347870*n^8 + 37889775*n^9 + 3897234*n^10 + 177147*n^11 + 39916800)*a(n) + (870112800*n + 1655958600*n^2 + 1805971896*n^3 + 561697416*n^5 + 1244162430*n^4 + 166255740*n^6 + 31125384*n^7 + 3346110*n^8 + 157464*n^9 + 199584000)*a(n + 1) + (70976400*n + 86362056*n^2 + 57212568*n^3 + 5161320*n^5 + 22352760*n^4 + 653184*n^6 + 34992*n^7 + 24393600)*a(n + 2) + (-468192*n-411840-198432*n^2-37152*n^3-2592*n^4)*a(n + 3) + 64*a(n + 4), a(2) = 75, a(3) = 122220}.

Differential equation satisfied by generating series A(t)=sum a(n) t^(3n)/(3n)!: {F(0) = 1, 16*t^5*(-2 + t^3)^3*(d^2/dt^2)F(t) + 8*t*(t^9-20*t^3 + 8)*(-2 + t^3)^2*(d/dt)F(t) + t^6*(t^3 + 10)*(t^3-4)*(-2 + t^3)^2*F(t)}.

a(n) ~ 3^(4*n+1/2) * n^(4*n) / (2^n * exp(4*n+1)). - Vaclav Kotesovec, Mar 11 2014

Example

One of the 75 2-regular 3-hypergraphs on 6 vertices: {1,2,3} {4,5,6} {1,2,4} {3,5,6}.

Crossrefs

Cf. A025035, A110101, A110103, A001205.

Sequence in context: A116527 A263064 A085404 * A003745 A301468 A068942

Adjacent sequences: A110097 A110098 A110099 * A110101 A110102 A110103

Keyword

easy,nonn

Author

Marni Mishna, Jul 11 2005

Extensions

Replaced broken link, Vaclav Kotesovec, Mar 11 2014

Status

approved