OFFSET
4,1
COMMENTS
The terms in the sequence alternate 2 even and 2 odd.
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-33,63,-66,36,-8).
FORMULA
a(n) = (Sum_{j=3..n/2} binomial(n,j)*binomial(j,2)) + (1/2)*binomial(n,n/2+1) * binomial(n/2+1,2), if n is even.
a(n) = Sum_{j=3..ceiling(n/2)} binomial(n,j)*binomial(j,2), if n is odd.
G.f.: x^4*(6 - 24*x + 33*x^2 - 18*x^3 + 4*x^4)/((1 - x)^3*(1 - 2*x)^3). - Stefano Spezia, Oct 09 2021
a(n) = A000554(n)/2. - Enrique Navarrete, Nov 16 2021
a(n) = binomial(n,2) * Stirling2(n-2,2). - Alois P. Heinz, Nov 16 2021
EXAMPLE
a(4) = 6 since we can write [4] as the following unions: {1,2,3} U {1,2,4}, {1,2,3} U {1,3,4}, {1,2,3} U {2,3,4}, {1,2,4} U {1,3,4}, {1,2,4} U {2,3,4}, {1,3,4} U {2,3,4}.
MATHEMATICA
nterms=50; Table[Binomial[n, 2]*StirlingS2[n-2, 2], {n, 4, nterms+3}] (* Paolo Xausa, Nov 20 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Enrique Navarrete, Oct 08 2021
STATUS
approved