[seqfan] Re: In search of a formula for a number triangle

[Robert G. Wilson v]

Seq.Fans,

The statement "Every positive number appears exactly once" is incorrect, if
the terms and the Mathematica coding are correctly presented. I find that
the following terms appear twice:
20,30,31,40,41,42,50,51,52,53,60,61,62,63,64,70,71,72,73,74,75,80,81,82,83,8
4,85,86,90,91,92,93,94,95,96,97,...,.
The following terms appear three
times:130,140,141,150,151,152,160,161,162,163,...,.
The following terms appear four times:
240,250,251,260,261,262,270,271,272,273,...,.
The following terms appear five times:
350,360,361,370,371,372,380,381,382,383,...,. etc.

Bob.

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Harvey P.
Dale
Sent: Monday, January 07, 2013 6:37 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: In search of a formula for a number triangle

Al:

	Does this Mma program properly generate the terms of the sequence?
	
	Flatten[Table[{n,Range[10n,10n+n-2]},{n,20}]]

	Best,

	Harvey
 

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Alonso Del
Arte
Sent: Monday, January 07, 2013 5:40 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] In search of a formula for a number triangle

The triangle of A077341

1

2 20

3 30 31

4 40 41 42

5 50 51 52 53

...

 19 190 191 ...

200 201 202 ...

 21 210 211 ...

...

and the related sequence A077342, initial rows of the triangle, has the
question "Can anyone derive a formula for a(n)?" I can't, but I believe I
may at least be able to figure out which a(n) = n. This is what I've come up
with:

a(n) = n when n > 10 * floor(n/10) + floor(n/10) - 2.

But of course this only takes into account the nearest previous row that
could possibly contain n. Is that enough or does this formula need to be
amended to take into account even earlier rows?

Al

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