This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A213385 a(n) = number of refinements of the partition n^1. (Formerly N0320) 6
 1, 2, 3, 7, 15, 43, 131, 468, 1776, 7559, 34022, 166749, 853823, 4682358, 26720781, 161074458, 1004485751, 6576974188, 44322716809, 311440019349, 2247888977510, 16819336465164, 128915407382036, 1021269823516449, 8261243728564640, 68848043979970646 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Consider the ranked poset L(n) of partitions defined in A002846. Then a(n) is the total number of paths of all lengths 0,1,...,n-1 that start at n^1 and end at a node in the poset. REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..50 Olivier Gérard, The ranked posets L(2),...,L(8) R. K. Guy, Letter to N. J. A. Sloane, June 24 1971: front, back [Annotated scanned copy, with permission] See sequence labeled H. EXAMPLE Referring to the ranked poset L(5) shown in the example in A002846, there are 15 paths that start at ooooo: end point / number of paths ooooo / 1 o oooo / 1 oo ooo / 1 o o ooo / 2 o oo oo / 2 o o o oo / 4 o o o o o / 4 Total a(5) = 15. MAPLE b:= proc(l) option remember; local n, i, j, t; n:=nops(l);       `if`(l[n]=1 and {l[1..n-1][]} minus {0}={}, 1,       add(`if`(l[i]=0, 0, add(`if`(l[j]=0 or i=j and l[j]<2, 0,       b([seq(`if`(t>n, 0, l[t])-`if`(t=i and t=j, 2, `if`(t=i or t=j,       1, `if`(t=i+j, -1, 0))), t=1..max(n, i+j))])), j=i..n)), i=1..n))     end: g:= proc(n, i, l)       `if`(n=0 and i=0, b(l), `if`(i=1, b([n, l[]]), add(g(n-i*j, i-1,       `if`(l=[] and j=0, l, [j, l[]])), j=0..n/i)))     end: a:= n-> g(n, n, []): seq(a(n), n=1..25);  # Alois P. Heinz, Jun 11 2012 MATHEMATICA b[l_List] := b[l] = Module[{n, i, j, t}, n = Length[l]; If[l[[n]] == 1 && Union[ l[[1 ;; n-1]]] ~Complement~ {0} == {}, 1, Sum[If[l[[i]] == 0, 0,  Sum[If[l[[j]] == 0 || i == j && l[[j]]<2, 0, b[Table[If[t>n, 0, l[[t]]] - Which[t == i && t == j, 2, t == i || t == j, 1, t == i+j, -1, True, 0], {t, 1, Max[n, i+j]}]]], {j, i, n}] ], {i, 1, n}]]]; g[n_, i_, l_List] := If[n == 0 && i == 0, b[l], If[i == 1, b[ Join[{n}, l]], Sum[g[n-i*j, i-1, If[l == {} && j == 0, l, Join[{j}, l]]], {j, 0, n/i}]]]; a[n_] := g[n, n, {}]; Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Feb 26 2015, after Alois P. Heinz *) CROSSREFS Cf. A002846, A213242, A213427. Sequence in context: A221547 A289471 A289470 * A161746 A045629 A034731 Adjacent sequences:  A213382 A213383 A213384 * A213386 A213387 A213388 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 10 2012 EXTENSIONS Definition clarified by David Applegate, Jun 10 2012 More terms from Alois P. Heinz, Jun 11 2012 Edited by Alois P. Heinz at the suggestion of Gus Wiseman, May 02 2016 STATUS approved

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