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!)
A332719 Index position of {n}^3 within the list of partitions of 3n in canonical ordering. 2
1, 3, 8, 19, 44, 93, 187, 357, 657, 1166, 2015, 3393, 5594, 9044, 14378, 22501, 34734, 52931, 79735, 118823, 175337, 256347, 371606, 534377, 762721, 1080979, 1521925, 2129330, 2961580, 4096006, 5634855, 7712558, 10505457, 14243772, 19227383, 25845241, 34600673 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The canonical ordering of partitions is described in A080577.
LINKS
FORMULA
a(n) ~ exp(2*Pi*sqrt(n/3)) / (4*Pi*sqrt(n)). - Vaclav Kotesovec, Feb 28 2020
EXAMPLE
a(2) = 8, because 222 has position 8 within the list of partitions of 6 in canonical ordering: 6, 51, 42, 411, 33, 321, 3111, 222, ... .
MAPLE
b:= proc(n, i) option remember;
`if`(n=0, 1, b(n-i, i)+g(n, i-1))
end:
g:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
`if`(i<1, 0, g(n-i, min(n-i, i))+g(n, i-1)))
end:
a:= n-> g(3*n$2)-b(3*n, n)+1:
seq(a(n), n=0..37);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, 1, b[n - i, i] + g[n, i - 1]];
g[n_, i_] := g[n, i] = If[n == 0 || i == 1, 1, If[i < 1, 0, g[n - i, Min[n - i, i]] + g[n, i - 1]]];
a[n_] := g[3n, 3n] - b[3n, n] + 1;
a /@ Range[0, 37] (* Jean-François Alcover, Jan 06 2021, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A371796 A191787 A347310 * A326599 A121551 A189391
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 20 2020
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 April 20 03:03 EDT 2024. Contains 371798 sequences. (Running on oeis4.)