The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A006046 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A006046

Total number of odd entries in first n rows of Pascal's triangle: a(0) = 0, a(1) = 1, a(2k) = 3*a(k), a(2k+1) = 2*a(k) + a(k+1). a(n) = Sum_{i=0..n-1} 2^wt(i).
(history; published version)

#209 by Alois P. Heinz at Wed Oct 23 12:54:44 EDT 2024

KEYWORD

nonn,nice,easy,look,changed

STATUS

proposed

approved

#208 by Ruud H.G. van Tol at Wed Oct 23 08:52:09 EDT 2024

STATUS

editing

proposed

#207 by Ruud H.G. van Tol at Wed Oct 23 08:49:54 EDT 2024

PROG

(PARI) a(n) = sum(i=0, n-1, 1<<hammingweight(i)); \\ Ruud H.G. van Tol, Oct 23 2024

Discussion

Wed Oct 23

08:52

Ruud H.G. van Tol: Please reject, was slow code that didn't add anything.

#206 by Ruud H.G. van Tol at Wed Oct 23 08:41:19 EDT 2024

PROG

(PARI) a(n) = sum(i=0, n-1, 1<<hammingweight(i)); \\ Ruud H.G. van Tol, Oct 23 2024

STATUS

approved

editing

#205 by Michael De Vlieger at Fri Aug 16 16:41:52 EDT 2024

STATUS

reviewed

approved

#204 by Stefano Spezia at Fri Aug 16 16:28:45 EDT 2024

STATUS

proposed

reviewed

#203 by Stefano Spezia at Fri Aug 16 16:28:40 EDT 2024

STATUS

editing

proposed

#202 by Stefano Spezia at Fri Aug 16 16:28:34 EDT 2024

LINKS

S. R. Finch, P. Sebah , and Z.-Q. Bai, <a href="http://arXiv.org/abs/0802.2654">Odd Entries in Pascal's Trinomial Triangle</a>, arXiv:0802.2654 [math.NT], 2008.

Philippe Flajolet, Peter Grabner, Peter Kirschenhofer, Helmut Prodinger , and Robert F. Tichy, <a href="https://doi.org/10.1016/0304-3975(92)00065-Y">Mellin Transforms And Asymptotics: Digital Sums</a>, Theoret. Computer Sci. 23 (1994), 291-314.

STATUS

proposed

editing

#201 by Michael De Vlieger at Fri Aug 16 15:46:26 EDT 2024

STATUS

editing

proposed

#200 by Michael De Vlieger at Fri Aug 16 15:46:24 EDT 2024

LINKS

Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2408.06817">Periodic minimum in the count of binomial coefficients not divisible by a prime</a>, arXiv:2408.06817 [math.NT], 2024. See p. 1.

STATUS

approved

editing