The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A048644 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A048644

Differences between partial sums of Gray code (A048641) and triangular numbers (A000217).
(history; published version)

#11 by Joerg Arndt at Sat Oct 29 11:50:26 EDT 2022

STATUS

proposed

approved

#10 by Michael De Vlieger at Sat Oct 29 11:05:56 EDT 2022

STATUS

editing

proposed

#9 by Michael De Vlieger at Sat Oct 29 11:05:53 EDT 2022

LINKS

Michael De Vlieger, <a href="/A048644/b048644.txt">Table of n, a(n) for n = 0..10000</a>

Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2210.10968">Identities and periodic oscillations of divide-and-conquer recurrences splitting at half</a>, arXiv:2210.10968 [cs.DS], 2022, p. 40.

MATHEMATICA

{0}~Join~MapIndexed[#1 - PolygonalNumber[First[#2]] &, Accumulate[Array[BitXor[#, Floor[#/2]] &, 65]]] (* Michael De Vlieger, Oct 29 2022 *)

STATUS

approved

editing

#8 by N. J. A. Sloane at Thu Oct 19 03:13:49 EDT 2017

EXTENSIONS

Corrected by _Don Reble (djr(AT)nk.ca), _, May 01 2006

Discussion

Thu Oct 19

03:13

OEIS Server: https://oeis.org/edit/global/2703

#7 by Bruno Berselli at Fri Oct 02 09:09:46 EDT 2015

STATUS

proposed

approved

#6 by Michel Marcus at Fri Oct 02 09:09:21 EDT 2015

STATUS

editing

proposed

#5 by Michel Marcus at Fri Oct 02 09:09:02 EDT 2015

PROG

(PARI) a(n) = sum(k=0, n, bitxor(k, k>>1)) - n*(n+1)/2; \\ Michel Marcus, Oct 02 2015

AUTHOR

_Antti Karttunen, _, Jul 14 1999

STATUS

approved

editing

#4 by N. J. A. Sloane at Fri May 19 03:00:00 EDT 2006

DATA

0, 0, 1, 0, 2, 4, 3, 0, 4, 8, 13, 16, 14, 12, 132, 540, 7, 0, 8, 16, 25, 32, 42, 52, 59, 64, 60, 56, 53, 48, 38, 28, 15, 0, 20160, 423360, 8164800, 125193600, 1172102400, 11935123200, 76281004800, 16, 32, 49, 64, 82, 100, 115, 128, 148, 168, 189, 208, 222, 236, 247, 256, 248, 240, 233, 224, 218, 212, 203, 192, 172, 152, 133, 112, 86, 60, 31, 0, 10461394944000, 428917192704000, 14781951055872000, 429147343392768000, 1409087130587136000032, 64

FORMULA

a(n) = sum(XORnos(j, floor(j/2)), j=0..n)-((jn^2+jn)/2).

CROSSREFS

Cf. A000217, A048461, A048643.

KEYWORD

easy,nonn,new

EXTENSIONS

Corrected by Don Reble (djr(AT)nk.ca), May 01 2006

#3 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

a(n) = sum(XORnos(j, floor(j/2)), j=0..n)-((j^2+j)/2).

KEYWORD

easy,nonn,new

#2 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

KEYWORD

easy,huge,nonn,new

AUTHOR

Antti.Karttunen@iki.fi (karttu@megabaud.fi (4.July.1999))

Antti Karttunen, Jul 14 1999