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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A327381 Number of colored integer partitions of n such that three colors are used and parts differ by size or by color. 6
 1, 3, 9, 19, 39, 72, 128, 216, 354, 563, 876, 1335, 1998, 2946, 4284, 6154, 8742, 12294, 17129, 23667, 32442, 44151, 59682, 80169, 107054, 142167, 187812, 246895, 323058, 420852, 545958, 705438, 908043, 1164609, 1488504, 1896174, 2407836, 3048255, 3847716 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 COMMENTS With offset 0 convolution cube of A000009(k+1). - George Beck, Jan 29 2021 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 3..10000 (terms 3..5000 from Alois P. Heinz) Wikipedia, Partition (number theory) FORMULA a(n) ~ exp(Pi*sqrt(n)) / (8 * n^(3/4)). - Vaclav Kotesovec, Sep 14 2019 G.f.: (-1 + Product_{m >= 1} (1 + x^m))^3. - George Beck, Jan 29 2021 MAPLE b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add((t->       b(t, min(t, i-1), k)*binomial(k, j))(n-i*j), j=0..min(k, n/i))))     end: a:= n-> (k-> add(b(n\$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(3): seq(a(n), n=3..45); MATHEMATICA b[n_, i_, k_] := b[n, i, k] = If[n==0, 1, If[i<1, 0, Sum[With[{t = n - i j}, b[t, Min[t, i - 1], k] Binomial[k, j]], {j, 0, Min[k, n/i]}]]]; a[n_] := With[{k = 3}, Sum[b[n, n, k-i] (-1)^i Binomial[k, i], {i, 0, k}]]; a /@ Range[3, 45] (* Jean-François Alcover, Dec 15 2020, after Alois P. Heinz *) CROSSREFS Column k=3 of A308680. Cf. A000009. Sequence in context: A080010 A135117 A038163 * A146819 A147213 A146441 Adjacent sequences:  A327378 A327379 A327380 * A327382 A327383 A327384 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 03 2019 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 June 26 05:02 EDT 2022. Contains 354877 sequences. (Running on oeis4.)