login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A347930 3-Springer numbers. 0
1, 1, 3, 16, 88, 625, 5527, 55760, 640540, 8329326, 120212331, 1905939913, 32987637967, 618591571085, 12489644875037, 270193806214360, 6235154917414954, 152875655211527878, 3968729594485785289, 108754865309750398187, 3137052120203959610759 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,3
COMMENTS
a(n) is also the volume of a certain flow polytope.
LINKS
Arvind Ayyer, Matthieu Josuat-Vergès, and Sanjay Ramassamy, Extensions of partial cyclic orders and consecutive coordinate polytopes, Ann. H. Lebesgue, 3 (2020), 275-297.
R. S. Gonzalez D'Leon, A. H. Morales, C. R. H. Hanusa, and M. Yip, Column convex matrices, G-cyclic orders, and flow polytopes, arXiv:2107.07326 [math.CO], 2021.
FORMULA
a(n) = Sum_{(x,y,z), x+y+z=n-2} ((n-2)!/(x!*y!*z!))*b(x,y,z), where b(x,y,z) are the 3-Entringer numbers defined by Ramassamy.
MAPLE
wcomps:=proc(n, k)
option remember;
local ocomps, ncomps, i;
ocomps:=combinat:-composition(n+k, k);
ncomps:={};
for i from 1 to nops(ocomps) do
ncomps:=ncomps union{[seq(ocomps[i][j]-1, j=1..k)]};
end do;
return [op(ncomps)];
end proc:
b:=proc(s) option remember;
local k;
k := nops(s);
if s = [seq(0, i=1..k)] then
return(1);
elif s[1]>0 then
return(add(b([s[2]+j, op(s[3..k]), s[1]-j-1]), j=0..s[1]-1));
else
return(0);
end if;
end proc:a:=proc(n) local N, S: N := n-2; S := wcomps(N, 3); return add(combinat:-multinomial(N, op(s))*b(s), s in S); end proc:seq(a(n), n=2..10);
CROSSREFS
Sequence in context: A163604 A151329 A356402 * A026111 A026330 A146963
KEYWORD
nonn
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 24 01:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)