# [seqfan] Re: 999999999888888887777777666666555554444333221

Sun Sep 21 01:11:14 CEST 2014

```There are 66712890763701234740813164553708284 terms in the sequence, if
I haven't made a mistake in my PARI program.

a(b) = {my(r=vector(b*(b-1)\2+1));
r = 1;
for(d=1,b-1,
forstep(n=d*(d+1)\2,d,-1,
r[n+1]+=binomial(n,d)*r[n-d+1]));
r}
v = a(10)
sum(n=2,#v,v[n])

By the number of digits, there are:

1, 1, 4, 5, 16, 82, 169, 541, 2272, 17965, 44407, 201751, 801515,
4890886, 52218595, 165519640, 835947970, 4290442728, 24096524166,
179566203960, 2739764737710, 9938147178960, 60997160143920,
331360222255920, 2154105076695000, 14308355062630200,
148898652724750500, 3043362702904524000, 12550859255187653400,
85564729840752162000, 446033694177751680000, 3160644316242901488000,
23904928042959835872000, 212227787619709557696000,
2872257514324824658032000, 85739562818913709978272000,
359325740171513750386752000, 1764944667656072549494848000,
10004773552120178696264400000, 69366429961366572294099840000,
546927620849236435395787200000, 6125589353511448076432816640000,
65850085550248066821652778880000, 1448701882105457470076361135360000,
65191584694745586153436251091200000

This is the vector returned by the function a above, except that that
i.e., zero if we wrote it as the empty string instead of the way we do.

The number of values in bases 2 through 9 is:

1, 5, 80, 14381, 40885253, 2163451135829, 2525544441942679544,
75742010013818779294524291

This also is not in the OEIS.

-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>

(My last post of the day, Gérard!)

Hello SeqFans,
Numbers showing, for any of their digit "d", exactly d copies of "d":

S=1,22,122,212,221,1333,3133,3313,3331,14444,41444,44144,44414,44441,...

Example:
312332 belongs to S as there are exactly
one "1", two "2" and three "3" in 312332.

The sequence is finite (how many
terms?) and the last term is, of course,

Best,
É.

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```