OFFSET
0,3
COMMENTS
A hypergraph is a T_0 hypergraph if for every two distinct nodes there exists a hyperedge containing one but not the other node.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
a(n) = binomial(n + 7, n) - 3*binomial(n + 3, n) + 2*binomial(n + 1, n) = n*(n - 1)*(n + 1)*(n^4 + 28*n^3 + 323*n^2 + 1988*n + 4572)/5040.
G.f.: x^2*(2-x)^2*(3-4*x+2*x^2)/(1-x)^8. - Colin Barker, Jun 25 2012
MAPLE
for n from 0 to 100 do printf(`%d, `, n*(n - 1)*(n + 1)*(n^4 + 28*n^3 + 323*n^2 + 1988*n + 4572)/5040) od:
MATHEMATICA
CoefficientList[Series[x^2*(2 - x)^2*(3 - 4*x + 2*x^2)/(1 - x)^8, {x, 0, 50}], x] (* G. C. Greubel, Oct 06 2017 *)
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 12, 68, 235, 636, 1478, 3088}, 33] (* Vincenzo Librandi, Oct 07 2017 *)
PROG
(PARI) x='x+O('x^50); concat([0, 0], Vec(x^2*(2-x)^2*(3-4*x+2*x^2)/(1-x)^8)) \\ G. C. Greubel, Oct 06 2017
(Magma) [n*(n-1)*(n+1)*(n^4+28*n^3+323*n^2+1988*n+ 4572)/5040: n in [0..35]]; // Vincenzo Librandi, Oct 07 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Jan 23 2001
EXTENSIONS
More terms from James A. Sellers, Jan 24 2001
STATUS
approved