The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A133037

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A133037

a(n) = A000931(n)^2.
(history; published version)

#31 by Ray Chandler at Mon Sep 30 15:06:28 EDT 2024

STATUS

proposed

approved

#30 by Kevin Ryde at Wed Sep 25 21:11:58 EDT 2024

STATUS

editing

proposed

#29 by Kevin Ryde at Wed Sep 25 21:10:26 EDT 2024

FORMULA

a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) for n >= 6.

STATUS

proposed

editing

Discussion

Wed Sep 25

21:11

Kevin Ryde: Recurrence already holds everywhere its terms exist.  No initial exceptions.

#28 by Michael A. Allen at Wed Sep 25 01:55:55 EDT 2024

STATUS

editing

proposed

#27 by Michael A. Allen at Wed Sep 25 01:54:41 EDT 2024

FORMULA

a(n) = a(n-2) + a(n-3) + 2*Sum_{r=8..n} ( A000930(r-8)*a(n+3-r) ) for n >= 3. - Michael A. Allen, Sep 25 2024

#26 by Joerg Arndt at Wed Sep 25 01:53:26 EDT 2024

STATUS

proposed

editing

#25 by Joerg Arndt at Wed Sep 25 01:53:16 EDT 2024

STATUS

editing

proposed

#24 by Joerg Arndt at Wed Sep 25 01:53:13 EDT 2024

NAME

Squares of members of the Padovan sequence A000931.

a(n) = A000931(n)^2.

#23 by Michael A. Allen at Wed Sep 25 01:49:57 EDT 2024

COMMENTS

a(n+3) is the number of tilings of an n-board (a board with dimensions n X 1) with (1/2,1/2;2)-combs and (1/2,1/2;3)-combs. A (w,g;m)-comb is a tile composed of m pieces of dimensions w X 1 separated horizontally by gaps of width g. - Michael A. Allen, Sep 25 2024

LINKS

Michael A. Allen and Kenneth Edwards, <a href="https://doi.org/10.1080/03081087.2022.2107979">Connections between two classes of generalized Fibonacci numbers squared and permanents of (0,1) Toeplitz matrices</a>, Lin. Multilin. Alg. 72:13 (2024) 2091-2103.

FORMULA

a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) for n >= 6.

a(n) = a(n-2) + a(n-3) + 2*Sum_{r=8..n} ( A000930(r-8)*a(n+3-r) ). - Michael A. Allen, Sep 25 2024

STATUS

approved

editing

#22 by Alois P. Heinz at Mon Apr 16 15:39:04 EDT 2018

STATUS

editing

approved