The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A000217 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A000217

Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n.
(history; published version)

#1849 by Charles R Greathouse IV at Sun Feb 16 08:32:20 EST 2025

LINKS

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/AbsoluteValue.html">Absolute Value</a>, <a href="httphttps://mathworld.wolfram.com/BinomialCoefficient.html">Binomial Coefficient</a>, <a href="httphttps://mathworld.wolfram.com/Composition.html">Composition</a>, <a href="httphttps://mathworld.wolfram.com/Distance.html">Distance</a>, <a href="httphttps://mathworld.wolfram.com/GolombRuler.html">Golomb Ruler</a>, <a href="httphttps://mathworld.wolfram.com/LineLinePicking.html">Line Line Picking</a>, <a href="httphttps://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>, <a href="httphttps://mathworld.wolfram.com/TriangularNumber.html">Triangular Number</a>, <a href="httphttps://mathworld.wolfram.com/TrinomialCoefficient.html">Trinomial Coefficient</a>, and <a href="httphttps://mathworld.wolfram.com/WienerIndex.html">Wiener Index</a>

Discussion

Sun Feb 16

08:32

OEIS Server: https://oeis.org/edit/global/3014

#1848 by N. J. A. Sloane at Thu Feb 06 12:28:04 EST 2025

STATUS

editing

approved

#1847 by N. J. A. Sloane at Thu Feb 06 12:28:02 EST 2025

FORMULA

a(n) = n^2 - a(n-1). - Marc Morgenegg, Feb 06 2025

STATUS

proposed

editing

#1846 by Marc Morgenegg at Thu Feb 06 10:03:23 EST 2025

STATUS

editing

proposed

Discussion

Thu Feb 06

10:06

Amiram Eldar: The new formula is the same as "a(n) + a(n+1) = (n+1)^2" that already appears above.

#1845 by Marc Morgenegg at Thu Feb 06 09:59:24 EST 2025

COMMENTS

a(n) = n^2 - a(n-1). - Marc Morgenegg, Feb 06 2025

FORMULA

a(n) = n^2 - a(n-1). - Marc Morgenegg, Feb 06 2025

#1844 by Marc Morgenegg at Thu Feb 06 09:57:22 EST 2025

COMMENTS

a(n) = n^2 - a(n-1). - Marc Morgenegg, Feb 06 2025

STATUS

proposed

editing

#1843 by Feihu Liu at Thu Feb 06 08:52:19 EST 2025

STATUS

editing

proposed

#1842 by Feihu Liu at Mon Feb 03 23:52:56 EST 2025

LINKS

Feihu Liu, Guoce Xin, and Chen Zhang, <a href="https://arxiv.org/abs/2412.18744">Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS</a>, arXiv:2412.18744 [math.CO], 2024. See pp. 13, 15, 29.

STATUS

approved

editing

#1841 by Michael De Vlieger at Tue Jan 21 18:23:11 EST 2025

STATUS

proposed

approved

#1840 by Stefano Spezia at Tue Jan 21 13:21:40 EST 2025

STATUS

editing

proposed