VOOZH about

URL: https://oeis.org/A091601

⇱ A091601 - OEIS

login
A091601
Number of compositions (ordered partitions) of n with designated summands.
1
1, 1, 3, 6, 14, 30, 69, 153, 345, 771, 1730, 3873, 8682, 19450, 43590, 97668, 218864, 490416, 1098933, 2462458, 5517870, 12364356, 27705944, 62083134, 139115247, 311727845, 698516370, 1565227653, 3507344882, 7859219406, 17610851898
OFFSET
0,3
LINKS
FORMULA
INVERT(DCONV(A000012, iINVERT(A000027)))
G.f.: 1/(1 - sum(k>0, x^k/(1-x^k+x^(2*k)))). - Vladeta Jovovic, Dec 04 2004
EXAMPLE
a(3)=6 because the compositions of 3 with designated summands are
3', 2'1', 1'2', 1'11, 11'1, 111'.
The composition 1121 corresponds to 1'12'1' and 11'2'1'.
MATHEMATICA
Table[l = Split /@ Flatten[Permutations /@ IntegerPartitions@n, 1];
Total[Table[x = l[[i]]; Product[Length@x[[j]], {j, Length[x]}], {i, Length[l]}]], {n, 0, 15}] (* Robert Price, Jun 07 2020 *)
CROSSREFS
Cf. A077285.
Sequence in context: A131244 A077926 A384599 * A339154 A063119 A218982
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jan 23 2004
STATUS
approved