The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A159797 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A159797

Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n-1.
(history; published version)

#26 by N. J. A. Sloane at Wed Feb 24 02:48:18 EST 2021

LINKS

David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="http://neilsloane.com/docA000695/tootha000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

Discussion

Wed Feb 24

02:48

OEIS Server: https://oeis.org/edit/global/2889

#25 by N. J. A. Sloane at Tue Nov 27 18:35:50 EST 2018

LINKS

David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="http://neilsloane.com/doc/tooth.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

Discussion

Tue Nov 27

18:35

OEIS Server: https://oeis.org/edit/global/2774

#24 by Charles R Greathouse IV at Sat Sep 26 01:17:05 EDT 2015

LINKS

N. J. A. Sloane, <a href="http://neilsloane.com/docwiki/toothlist.htmlCatalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>

Discussion

Sat Sep 26

01:17

OEIS Server: https://oeis.org/edit/global/2460

#23 by N. J. A. Sloane at Fri Nov 28 21:59:04 EST 2014

STATUS

proposed

approved

#22 by Jon E. Schoenfield at Fri Nov 28 03:39:12 EST 2014

STATUS

editing

proposed

#21 by Jon E. Schoenfield at Fri Nov 28 03:39:10 EST 2014

COMMENTS

The triangle sums, see A180662 for their definitions, link the triangle A159797 with eleven sequences, see the crossrefs. - [__Johannes W. Meijer_, May 20 2011]

FORMULA

Given m = floor( (sqrt(8*n+1)-1)/2 ), then a(n) = m + (n - m*(m+1)/2)*(m-1). - [__Carl R. White_, Jul 24 2010]

CROSSREFS

Cf.: A006002 (row sums). [From _- _R. J. Mathar_, Jul 17 2009]

Cf. A163282, A163283, A163284, A163285. [From _- _Omar E. Pol_, Nov 18 2009]

STATUS

proposed

editing

#20 by Derek Orr at Wed Nov 26 11:02:23 EST 2014

STATUS

editing

proposed

#19 by Derek Orr at Wed Nov 26 11:02:03 EST 2014

COMMENTS

T(n,k) is the number of distinct sums in the direct sum of {1, 2, ... n} with itself k times for 1 <= k <= n+1, i.e., g., T(5,3) = the number of distinct sums in the direct sum {1,2,3,4,5} + {1,2,3,4,5} + {1,2,3,4,5}. The sums range from 1+1+1=3 to 5+5+5=15. So there are 13 distinct sums. - Derek Orr, Nov 26 2014

Discussion

Wed Nov 26

11:02

Derek Orr: Thanks Michel.

#18 by Joerg Arndt at Wed Nov 26 10:57:10 EST 2014

STATUS

proposed

editing

#17 by Michel Marcus at Wed Nov 26 00:58:05 EST 2014

STATUS

editing

proposed

Discussion

Wed Nov 26

10:57

Joerg Arndt: yes