A282715 Number of nonzero entries in row n of the base-3 generalized Pascal triangle P_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
Offset: 0
Keywords
Examples
The number of nonzero entries in the n-th 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
Links
- Lars Blomberg, Table of n, a(n) for n = 0..10000
- Julien Leroy, Michel Rigo, and Manon Stipulanti, Counting the number of non-zero coefficients in rows of generalized Pascal triangles, Discrete Mathematics 340 (2017), 862-881, Section 7.
- Julien Leroy, Michel Rigo, and Manon Stipulanti, Counting Subwords Occurrences in Base-b Expansions, arXiv:1705.10065 [math.CO], 2017.
- Julien Leroy, Michel Rigo, and Manon Stipulanti, Counting Subwords Occurrences in Base-b Expansions, Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A13.
- Manon Stipulanti, Convergence of Pascal-Like Triangles in Parry-Bertrand Numeration Systems, arXiv:1801.03287 [math.CO], 2018.
Programs
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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
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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}] (* Jean-François Alcover, Dec 28 2017 *)
Formula
Leroy et al. (2017) state some conjectured recurrences.
Extensions
More terms from Lars Blomberg, Mar 03 2017
Comments