The Twelve Days of Christmas and A003990, A002620, etc.

[N. J. A. Sloane]

The two sequences in question are A003991 and (as Franklin T. Adams-Watters
already pointed out) A002620.

I will add comments about the song to those two entries.

NJAS

>Date: Fri, 17 Jun 2005 17:39:25 -0400
>From: Alonso Del Arte <alonso.delarte at gmail.com>
>Reply-To: Alonso Del Arte <alonso.delarte at gmail.com>
>To: seqfan at ext.jussieu.fr
>Subject: The Twelve Days of Christmas and A003990, A002620, etc.

>As furniture stores gear up to celebrate Christmas in July, I was
>thinking about the gift totals in the song "The Twelve Days of
>Christmas."
>
>On the first day, you have one partridge in a pear tree. On the second
>day, you have two partridges in pear trees and two turtle doves. By
>the twelfth day, you have 12 partridges in pear trees, 22 turtle
>doves, 30 French hens, 36 calling birds, 40 golden rings, 42 geese
>a-laying, 42 swans a-swimming, 40 maids a-milking, 36 ladies dancing,
>30 lords a-leaping, 22 pipers piping and 12 drummers drumming. I
>expected to find this sequence in the OEIS, but I wasn't expecting
>five results, none of which mention this famous song. I'm not sure
>under which one it would be appropriate to file the comment.
>
>I also looked up 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, the
>largest number of a distinct gift you'd have on the n-th day. This
>yielded seven results, and extending the sequence to n = 15 (I have no
>idea what the extra gifts would be) still gives five results.
>
>Alonso