It is done --- see A180437,8,9. The related problem for Sturmian sequences (2 symbols) was not mentioned in OEIS. I have amended A005598, A002088, A000010 appropriately, and added A180444. [Unfortunately an entirely superfluous "that is are" has crept into the additions to A002088, A000010 --- I daren't try to delete it in case that causes a tangle ...] Fred Lunnon On 9/5/10, N. J. A. Sloane <njas@research.att.com> wrote:

On Aug 20 Fred posted this message, which was followed by several related messages:

The counts of 3-D billiard words of length n with k = 1,2,3 descendants of length n+1, for n = 0,...,19 are respectively

0, 0, 0, 6, 24, 78, 186, 372, 876, 1632, 3024, 5310, 8496, 13344, 21186, 31878, 46752, 66936, 94800, 130194, when k = 1;

0, 0, 6, 18, 36, 78, 150, 306, 420, 792, 1338, 2082, 3228, 4830, 7050, 9954, 13920, 18738, 24666, 32610, when k = 2;

1, 3, 3, 3, 9, 15, 33, 63, 153, 219, 261, 351, 585, 879, 933, 1233, 1401, 1899, 2301, 3111, when k = 3;

Allan's sequence is the sum of the last two; note that his 15 should read 21.

Fred Lunnon

Could someone please submit these three to the OEIS (Fred?), so that I can clean up these emails?

Thanks!

Neil

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