A015743 Number of 8's in all the partitions of n into distinct parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 5, 5, 7, 9, 10, 13, 15, 18, 22, 27, 31, 37, 44, 51, 61, 71, 82, 95, 111, 128, 148, 171, 195, 225, 258, 295, 337, 384, 437, 497, 565, 639, 724, 818, 923, 1042, 1173, 1319, 1483, 1665

Offset

1,11

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 2000 terms from Robert Price)

Formula

G.f.: x^8*Product_{j>=1} (1+x^j)/(1+x^8). - Emeric Deutsch, Apr 17 2006

Example

a(11)=2 because in the 12 (=A000009(11)) partitions of 11 into distinct parts, namely [11], [10,1], [9,2], [8,3], [8,2,1], [7,4], [7,3,1], [6,5], [6,4,1], [6,3,2], [5,4,2] and [5,3,2,1], altogether we have two parts equal to 8.

Maple

g:=x^8*product(1+x^j, j=1..60)/(1+x^8): gser:=series(g, x=0, 57): seq(coeff(gser, x, n), n=1..54); # Emeric Deutsch, Apr 17 2006

Mathematica

Table[Count[Flatten@Select[IntegerPartitions[n], DeleteDuplicates[#] == # &], 8], {n, 54}] (* Robert Price, Jun 13 2020 *)

Crossrefs

Sequence in context: A342499 A325096 A261771 * A015755 A096443 A126442

Adjacent sequences: A015740 A015741 A015742 * A015744 A015745 A015746

Keyword

nonn

Author

Clark Kimberling

Status

approved