cp's OEIS Frontend

A282720 Number of nonzero terms in first n rows of the base-2 generalized Pascal triangle P_2 (see A282714).

%I A282720 #26 Oct 29 2023 09:47:26
%S A282720 0,1,3,6,9,13,18,23,27,32,39,47,54,61,69,76,81,87,96,107,117,128,141,
%T A282720 153,162,171,183,196,207,217,228,237,243,250,261,275,288,303,321,338,
%U A282720 351,365,384,405,423,440,459,475,486,497,513,532,549,567
%N A282720 Number of nonzero terms in first n rows of the base-2 generalized Pascal triangle P_2 (see A282714).
%C A282720 Same as partial sums of (A007306 with initial 1 omitted).
%H A282720 Michael De Vlieger, <a href="/A282720/b282720.txt">Table of n, a(n) for n = 0..3000</a>
%H A282720 Julien Leroy, Michel Rigo, and Manon Stipulanti, <a href="https://doi.org/10.37236/6581">Behavior of Digital Sequences Through Exotic Numeration Systems</a>, Electronic Journal of Combinatorics 24(1) (2017), #P1.44.
%H A282720 Julien Leroy, Michel Rigo, and Manon Stipulanti, <a href="https://arxiv.org/abs/1705.10065">Counting Subwords Occurrences in Base-b Expansions</a>, arXiv:1705.10065 [math.CO], 2017.
%H A282720 Julien Leroy, Michel Rigo, and Manon Stipulanti, <a href="http://math.colgate.edu/~integers/sjs13/sjs13.Abstract.html">Counting Subwords Occurrences in Base-b Expansions</a>, Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A13.
%H A282720 Manon Stipulanti, <a href="https://arxiv.org/abs/1801.03287">Convergence of Pascal-Like Triangles in Parry-Bertrand Numeration Systems</a>, arXiv:1801.03287 [math.CO], 2018.
%t A282720 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 *)
%o A282720 (PARI) f(n) = n--; sum(k=0, n, binomial(n+k, n-k)%2);
%o A282720 a(n) = sum(k=0, n, f(k)); \\ _Michel Marcus_, Oct 29 2023
%Y A282720 Cf. A282714, A007306.
%K A282720 nonn
%O A282720 0,3
%A A282720 _N. J. A. Sloane_, Mar 03 2017