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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A332720 Index position of {3}^n within the list of partitions of 3n in canonical ordering. 2
 1, 1, 5, 19, 59, 150, 349, 745, 1515, 2936, 5514, 10036, 17851, 31039, 53006, 88943, 147057, 239701, 385885, 613855, 966137, 1505137, 2323124, 3553914, 5392315, 8117758, 12131618, 18003740, 26543030, 38886999, 56633453, 82009410, 118113488, 169229009, 241264461 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The canonical ordering of partitions is described in A080577. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..4000 Wikipedia, Integer Partition FORMULA a(n) ~ exp(Pi*sqrt(2*n)) / (4*3^(3/2)*n). - Vaclav Kotesovec, Feb 28 2020 EXAMPLE a(2) = 5, because 33 has position 5 within the list of partitions of 6 in canonical ordering: 6, 51, 42, 411, 33, 321, 3111, 222, ... . MAPLE b:= proc(n) option remember; `if`(n=0, 1, b(n-1)+g(3*n, 2)) 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(n)+1: seq(a(n), n=0..35); MATHEMATICA b[n_] := b[n] = If[n == 0, 1, b[n - 1] + g[3n, 2]]; 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[n] + 1; a /@ Range[0, 35] (* Jean-François Alcover, Jan 06 2021, after Alois P. Heinz *) CROSSREFS Cf. A000041, A080577, A322761, A330661, A332706, A332719. Sequence in context: A029861 A224034 A107179 * A092442 A341711 A328543 Adjacent sequences: A332717 A332718 A332719 * A332721 A332722 A332723 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.

Last modified August 12 17:00 EDT 2024. Contains 375113 sequences. (Running on oeis4.)