The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A172225 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A172225

Number of ways to place 2 nonattacking wazirs on an n X n board.
(history; published version)

#25 by R. J. Mathar at Thu Apr 11 13:55:13 EDT 2024

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editing

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#24 by R. J. Mathar at Thu Apr 11 13:55:10 EDT 2024

FORMULA

a(n) = A232833(n,2). - R. J. Mathar, Apr 11 2024

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#23 by Harvey P. Dale at Sun Jun 04 10:51:42 EDT 2023

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#22 by Harvey P. Dale at Sun Jun 04 10:51:40 EDT 2023

MATHEMATICA

LinearRecurrence[{5, -10, 10, -5, 1}, {0, 2, 24, 96, 260}, 40] (* Harvey P. Dale, Jun 04 2023 *)

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#21 by Michael De Vlieger at Mon Aug 01 08:08:43 EDT 2022

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#20 by Jon E. Schoenfield at Mon Aug 01 04:23:42 EDT 2022

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proposed

#19 by Jon E. Schoenfield at Mon Aug 01 04:23:40 EDT 2022

REFERENCES

Christian Poisson, Echecs et mathematiques, Rex Multiplex 29/1990, p. 829.

FORMULA

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Vincenzo Librandi, Apr 30 2013

PROG

(MAGMAMagma) I:=[0, 2, 24, 96, 260]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]]; /* or */ [n*(n-1)*(n^2+n-4)/2: n in [1..40]]; // Vincenzo Librandi, Apr 30 2013

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#18 by Wesley Ivan Hurt at Fri Apr 10 02:02:23 EDT 2020

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#17 by Wesley Ivan Hurt at Fri Apr 10 02:02:07 EDT 2020

COMMENTS

A wazir is a (fairy chess) leaper [0,1].

FORMULA

Explicit formula (Christian Poisson, 1990): a(n) = n*(n-1)*(n^2+n-4)/2.

G.f.: 2x2*x^2*(2x2*x^2-7x7*x-1)/(x-1)^5 [From _. - _Vaclav Kotesovec_, Mar 25 2010]

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editing

#16 by R. J. Mathar at Tue Jan 09 04:13:41 EST 2018

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editing

approved