Ternary analogue of A094913?

[Maximilian Hasler]

Sorry for flooding you mailboxes... another (last(?)) word on this:
(seems to indicate another erroneous sequence)

When I add 1 to the sequence (i.e. include the empty word) FOR BASE=4,
 then I get the sequence

vector(20,n,A094913(n,4)+1)
%4 = [2, 4, 7, 11, 15, 20, 26, 33, 41, 50, 60, 71, 83, 96, 110, 125,
141, 157, 174, 192]

which matches up to the "141" the sequence

http://www.research.att.com/~njas/sequences/A077169 : Initial terms of
rows of A077168.
which then goes on with 158...
However, due to the manner that (IMHO slightly obscure) sequence
(A077168) is defined:
%N A077168 Triangle formed by grouping the natural numbers so that the
n-th group contains n numbers whose product is a factorial.

it could be possible that there is an error in A077169 - I'm very sceptic about:
%F A077169 For n>3, a(n) = (n^2-n+10)/2.
IMHO this assumes that the first r-1 terms of the r-th row of A077168
are consecutive integers and the last term (A077170(r) (or r-1 ?
notice obscure offset=0)) is the next possible factorial divided by
their product - which (as I see it) becomes (obviously!?) wrong when
one reaches a line containing one of the previously used big numbers
(A077170).

M.H.

> Unfortunately, that sequence lacks any comment or example or
> explanation, I have some trouble in understanding its definition
> (maybe my brain is too old or just a bit tired...) - could anybody
> familiar with these notations elaborate on that ?
> (are the [] the floor function? what is p(x) ?)
> Thanks in advance.
> M.H.
>
>
> On Dec 11, 2007 8:48 AM, Maximilian Hasler <maximilian.hasler at gmail.com> wrote:
> > I offer PARI code and some values based on the reasoning found in A094913:
> >
> > A094913(n,base=2)=sum(k=1,n,min(base^k,n-k+1))
> >
> > vector(20,n,A094913(n))
> > %1 = [1, 3, 5, 8, 12, 16, 21, 27, 34, 42, 50, 59, 69, 80, 92, 105,
> > 119, 134, 150, 166]
> >
> > vector(20,n,A094913(n,3))
> > %2 = [1, 3, 6, 9, 13, 18, 24, 31, 39, 48, 57, 67, 78, 90, 103, 117,
> > 132, 148, 165, 183]
> >
> > M.H.
> >
>



Dear M.H.,

yes [] is almost always the floor function
in the math literature.  the word floor is a recent innovation

and p(i) here means the i-th prime, as you guessed.