The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A005319 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A005319

a(n) = 6*a(n-1) - a(n-2).
(history; published version)

#134 by Charles R Greathouse IV at Sun Feb 16 08:32:28 EST 2025

LINKS

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/EdgeCover.html">Edge Cover</a>

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/TriangularSnakeGraph.html">Triangular Snake Graph</a>

Discussion

Sun Feb 16

08:32

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

#133 by N. J. A. Sloane at Thu Jul 25 14:05:11 EDT 2024

STATUS

proposed

approved

#132 by Greg Dresden at Thu Jul 25 10:33:13 EDT 2024

STATUS

editing

proposed

#131 by Greg Dresden at Thu Jul 25 10:32:39 EDT 2024

COMMENTS

For n>0, a(n) is the sum of 4*n consecutive powers of the silver ratio 1+sqrt(2), starting at (1+sqrt(2))^(-2*n) and ending at (1+sqrt(2))^(2*n-1). - Greg Dresden and Ruxin Sheng, Jul 25 2024

#130 by Greg Dresden at Thu Jul 25 10:31:53 EDT 2024

COMMENTS

For n>0, a(n) is the sum of 4*n consecutive powers of the silver ratio 1+sqrt(2), starting at (1+sqrt(2))^(-2*n) and ending at (1+sqrt(2))^(2*n-1). - Greg Dresden, and Ruxin Sheng, Jul 25 2024

#129 by Greg Dresden at Thu Jul 25 10:31:09 EDT 2024

COMMENTS

For n>0, a(n) is the sum of 4*n consecutive powers of the silver ratio 1+sqrt(2), starting at (1+sqrt(2))^(-2*n) and ending at (1+sqrt(2))^(2*n-1). - Greg Dresden, Jul 25 2024

STATUS

approved

editing

#128 by Michael De Vlieger at Fri Apr 19 17:38:41 EDT 2024

STATUS

reviewed

approved

#127 by Stefano Spezia at Fri Apr 19 12:53:14 EDT 2024

STATUS

proposed

reviewed

#126 by Joerg Arndt at Fri Apr 19 03:57:02 EDT 2024

STATUS

editing

proposed

#125 by Joerg Arndt at Fri Apr 19 03:56:50 EDT 2024

FORMULA

(-1)^(n+1) = A090390(n+1) + A001542(n+1) + A046729(n) - a(n) (conjectured). Generated by the floretion - .5'i + .5'j - .5i' + .5j' + 'ii' - 'jj' - 2'kk' + 'ij' + .5'ik' + 'ji' + .5'jk' + .5'ki' + .5'kj' + e. - Creighton Dement, Nov 17 2004

a(n) = 2*A000129(2n2*n). - Tanya Khovanova and MIT PRIMES STEP senior group, Apr 17 2024

STATUS

proposed

editing