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

0,3

Comments

Same as partial sums of (A007306 with initial 1 omitted).

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.

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 *)

Prog

(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

Crossrefs

Cf. A282714, A007306.

Sequence in context: A310158 A076523 A310159 * A129403 A323622 A154287

Adjacent sequences: A282717 A282718 A282719 * A282721 A282722 A282723

Keyword

nonn

Author

N. J. A. Sloane, Mar 03 2017

Status

approved