A282720 Number of nonzero terms in first n rows of the base-2 generalized Pascal triangle P_2 (see A282714).
0, 1, 3, 6, 9, 13, 18, 23, 27, 32, 39, 47, 54, 61, 69, 76, 81, 87, 96, 107, 117, 128, 141, 153, 162, 171, 183, 196, 207, 217, 228, 237, 243, 250, 261, 275, 288, 303, 321, 338, 351, 365, 384, 405, 423, 440, 459, 475, 486, 497, 513, 532, 549, 567
Offset: 0
Keywords
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..3000
- Julien Leroy, Michel Rigo, and Manon Stipulanti, Behavior of Digital Sequences Through Exotic Numeration Systems, Electronic Journal of Combinatorics 24(1) (2017), #P1.44.
- 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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Mathematica
Accumulate@ Prepend[Array[Sum[Mod[Binomial[# + k - 1, 2 k], 2], {k, 0, #}] &, 53], 0] (* Michael De Vlieger, Sep 04 2018, after Jean-François Alcover at A007306 *) -
PARI
f(n) = n--; sum(k=0, n, binomial(n+k, n-k)%2); a(n) = sum(k=0, n, f(k)); \\ Michel Marcus, Oct 29 2023
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