The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A087289

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A087289

a(n) = 2^(2*n+1) + 1.
(history; published version)

#91 by Alois P. Heinz at Sat Aug 24 21:45:06 EDT 2024

STATUS

proposed

approved

#90 by Jason Yuen at Sat Aug 24 21:13:23 EDT 2024

STATUS

editing

proposed

#89 by Jason Yuen at Sat Aug 24 21:13:19 EDT 2024

COMMENTS

An unpublished result due to Stephen Suen, David desJardins, and W. Edwin Clark. This is the case k = 2, q = 2 of their formula q^((n+1)*k) * (1 - 1/q^(k-1) + (q-1)/q^((n+1)*k)) for the number of ordered k-tuples (f_1, ..., f_k) of polynomials in GF(q)[x] such that deg(f_i) <= n for all i and gcd((f_1, ..., f_k) = 1.

STATUS

approved

editing

#88 by R. J. Mathar at Tue Aug 06 09:30:29 EDT 2024

STATUS

editing

approved

#87 by R. J. Mathar at Tue Aug 06 09:30:23 EDT 2024

LINKS

K. Morrison, <a href="https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.701.4944&rep=rep1&type=pdf/d980bc1fc0f75f630be96e7a829478d910109c67">Random polynomials over finite fields</a>

STATUS

approved

editing

#86 by N. J. A. Sloane at Sat Aug 20 13:30:42 EDT 2022

STATUS

proposed

approved

#85 by Alois P. Heinz at Thu Aug 18 16:22:55 EDT 2022

STATUS

editing

proposed

#84 by Alois P. Heinz at Thu Aug 18 16:21:36 EDT 2022

COMMENTS

An unpublished result due to Stephen Suen, David desJardins, and _W. Edwin Clark_. This is the case k = 2, q = 2 of their formula q^((n+1)*k) * (1 - 1/q^(k-1) + (q-1)/q^((n+1)*k)) for the number of ordered k-tuples (f_1, ..., f_k) of polynomials in GF(q)[x] such that deg(f_i) <= n for all i and gcd((f_1, ..., f_k) = 1.

#83 by Alois P. Heinz at Thu Aug 18 16:18:36 EDT 2022

LINKS

K. Morrison, <a href="https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.701.4944&rep=rep1&type=pdf">Random polynomials over finite fields</a>

#82 by Alois P. Heinz at Thu Aug 18 16:18:10 EDT 2022

LINKS

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).