The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A238537 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A238537

A fourth-order linear divisibility sequence related to the Pell numbers.
(history; published version)

#35 by Susanna Cuyler at Tue Nov 09 18:39:46 EST 2021

STATUS

proposed

approved

#34 by Michael De Vlieger at Tue Nov 09 17:58:16 EST 2021

STATUS

editing

proposed

#33 by Michael De Vlieger at Tue Nov 09 17:58:13 EST 2021

LINKS

Michael De Vlieger, <a href="/A238537/b238537.txt">Table of n, a(n) for n = 1..654</a>

#32 by Michael De Vlieger at Tue Nov 09 17:56:17 EST 2021

LINKS

E. L. Roettger and H. C. Williams, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Roettger/roettger12.html">Appearance of Primes in Fourth-Order Odd Divisibility Sequences</a>, J. Int. Seq., Vol. 24 (2021), Article 21.7.5.

STATUS

approved

editing

#31 by N. J. A. Sloane at Sat Feb 06 21:50:34 EST 2021

STATUS

proposed

approved

#30 by Jon E. Schoenfield at Sat Feb 06 18:13:40 EST 2021

STATUS

editing

proposed

#29 by Jon E. Schoenfield at Sat Feb 06 18:13:38 EST 2021

FORMULA

a(n) = (1/5)*A000129(3*n)*A001333(n).

a(n) = (1/(20*sqrt(2)))*((1 + sqrt(2))^(3*n) - (1 - sqrt(2))^(3*n))*( (1 + sqrt(2))^n + (1 - sqrt(2))^n ).

O.g.f. : x*(1 + 14*x + x^2)/( (1 + 6*x + x^2)*(1 - 34*x + x^2) ).

Recurrence equation: a(n) = 28*a(n-1) + 202*a(n-2) + 28*a(n-3) - a(n-4).

STATUS

approved

editing

#28 by Michel Marcus at Sat Nov 02 10:44:21 EDT 2019

STATUS

reviewed

approved

#27 by Joerg Arndt at Sat Nov 02 10:42:56 EDT 2019

STATUS

proposed

reviewed

#26 by Jean-François Alcover at Sat Nov 02 10:18:50 EDT 2019

STATUS

editing

proposed