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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A184641 Number of partitions of n having no parts with multiplicity 6. 8
 1, 1, 2, 3, 5, 7, 10, 15, 21, 29, 40, 54, 72, 96, 127, 166, 216, 279, 358, 457, 580, 735, 924, 1159, 1446, 1799, 2228, 2752, 3388, 4158, 5087, 6207, 7551, 9165, 11093, 13401, 16144, 19412, 23286, 27882, 33310, 39727, 47289, 56191, 66647, 78923, 93299 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) = A000041(n) - A183563(n). a(n) = A183568(n,0) - A183568(n,6). G.f.: Product_{j>0} (1-x^(6*j)+x^(7*j))/(1-x^j). EXAMPLE a(6) = 10, because 10 partitions of 6 have no parts with multiplicity 6: [1,1,1,1,2], [1,1,2,2], [2,2,2], [1,1,1,3], [1,2,3], [3,3], [1,1,4], [2,4], [1,5], [6]. MAPLE b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, [0, 0],       add((l->`if`(j=6, [l[1]\$2], l))(b(n-i*j, i-1)), j=0..n/i)))     end: a:= n-> (l-> l[1]-l[2])(b(n, n)): seq(a(n), n=0..50); MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[Function[l, If[j == 6, {l[[1]], l[[1]]}, l]][b[n - i*j, i - 1]], {j, 0, n/i}]]]; a[n_] := b[n, n][[1]] - b[n, n][[2]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Apr 30 2018, after Alois P. Heinz *) CROSSREFS Cf. A000041, A183563, A183568, A007690, A116645, A118807, A184639, A184640, A184642, A184643, A184644, A184645. Sequence in context: A240573 A160571 A238543 * A225490 A076972 A301756 Adjacent sequences:  A184638 A184639 A184640 * A184642 A184643 A184644 KEYWORD nonn AUTHOR Alois P. Heinz, Jan 18 2011 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 May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)