

A282715


Number of nonzero entries in row n of the base3 generalized Pascal triangle P_3.


3



1, 2, 2, 3, 3, 4, 3, 4, 3, 4, 5, 6, 5, 4, 6, 7, 7, 6, 4, 6, 5, 7, 6, 7, 5, 6, 4, 5, 7, 8, 8, 7, 10, 10, 11, 9, 7, 8, 10, 7, 5, 8, 11, 10, 9, 10, 13, 12, 13, 10, 12, 11, 11, 8, 5, 8, 7, 10, 9, 11, 8, 10, 7, 10, 12, 13, 11, 8, 11, 13, 12, 10, 7, 10, 8, 11, 9, 10
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OFFSET

0,2


COMMENTS

It would be nice to have an entry for the triangle P_3 itself (compare A282714 which gives the base2 triangle P_2).


LINKS

Lars Blomberg, Table of n, a(n) for n = 0..10000
Julien Leroy, Michel Rigo, Manon Stipulanti, Counting the number of nonzero coefficients in rows of generalized Pascal triangles, Discrete Mathematics 340 (2017), 862881, Section 7.
Julien Leroy, Michel Rigo, Manon Stipulanti, Counting Subwords Occurrences in Baseb Expansions, arXiv:1705.10065 [math.CO], 2017.
Julien Leroy, Michel Rigo, Manon Stipulanti, Counting Subwords Occurrences in Baseb Expansions, Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A13.
Manon Stipulanti, Convergence of PascalLike Triangles in ParryBertrand Numeration Systems, arXiv:1801.03287 [math.CO], 2018.


FORMULA

Leroy et al. (2017) state some conjectured recurrences.


EXAMPLE

The number of nonzero entries in the nth row of the following triangle:
1
1 1
1 0 1
1 1 0 1
1 2 0 0 1
1 1 1 0 0 1
1 0 1 0 0 0 1
1 1 1 0 0 0 0 1
1 0 2 0 0 0 0 0 1
1 1 0 2 0 0 0 0 0 1
1 2 0 1 1 0 0 0 0 0 1
1 1 1 1 0 1 0 0 0 0 0 1
1 2 0 2 1 0 0 0 0 0 0 0 1
1 3 0 0 3 0 0 0 0 0 0 0 0 1


MAPLE

# reuses code snippets of A282714
A282715 := proc(n)
add(min(P(n, k, 3), 1), k=0..n) ;
end proc:
seq(A282715(n), n=0..100) ; # R. J. Mathar, Mar 03 2017


MATHEMATICA

row[n_] := Module[{bb, ss}, bb = Table[IntegerDigits[k, 3], {k, 0, n}]; ss = Subsets[Last[bb]]; Prepend[Count[ss, #]& /@ bb // Rest, 1]];
a[n_] := Count[row[n], _?Positive];
Table[a[n], {n, 0, 100}] (* JeanFrançois Alcover, Dec 28 2017 *)


CROSSREFS

Cf. A007306, A282714.
Sequence in context: A269989 A057935 A292042 * A124831 A105096 A157790
Adjacent sequences: A282712 A282713 A282714 * A282716 A282717 A282718


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Mar 02 2017


EXTENSIONS

More terms from Lars Blomberg, Mar 03 2017


STATUS

approved



