The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A316726

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A316726

The number of ways to tile (with squares and rectangles) a 2 X (n+2) strip with the upper left and upper right squares removed.
(history; published version)

#22 by Susanna Cuyler at Mon Jul 16 09:13:09 EDT 2018

STATUS

proposed

approved

#21 by Michel Marcus at Mon Jul 16 08:18:16 EDT 2018

STATUS

editing

proposed

#20 by Michel Marcus at Mon Jul 16 08:18:07 EDT 2018

MATHEMATICA

CoefficientList[ Series[(-x^2 + 1)/(x^4 - 4x^2 - 2x + 1), {x, 0, 27}], x] (* or *) LinearRecurrence[{2, 4, 0, -1}, {2, 4, 15, 46}, 27] (* Robert G. Wilson v, Jul 15 2018 *)

STATUS

proposed

editing

#19 by Colin Barker at Mon Jul 16 07:42:07 EDT 2018

STATUS

editing

proposed

#18 by Robert G. Wilson v at Sun Jul 15 14:25:44 EDT 2018

MATHEMATICA

CoefficientList[ Series[(-x^2 + 1)/(x^4 - 4x^2 - 2x + 1), {x, 0, 27}], x] (* or *)LinearRecurrence[{2, 4, 0, -1}, {2, 4, 15, 46}, 27] (* Robert G. Wilson v, Jul 15 2018 *)

STATUS

proposed

editing

#17 by Colin Barker at Sun Jul 15 13:43:36 EDT 2018

STATUS

editing

proposed

#16 by Colin Barker at Sun Jul 15 13:43:08 EDT 2018

LINKS

Colin Barker, <a href="/A316726/b316726.txt">Table of n, a(n) for n = 0..1000</a>

STATUS

approved

editing

#15 by N. J. A. Sloane at Sun Jul 15 13:29:08 EDT 2018

STATUS

proposed

approved

#14 by Jon E. Schoenfield at Sat Jul 14 14:25:12 EDT 2018

STATUS

editing

proposed

#13 by Jon E. Schoenfield at Sat Jul 14 14:24:39 EDT 2018

NAME

The number of ways to tile (with squares and rectangles) a 2 by X (n+2) strip with the upper- left and upper- right squares removed.

COMMENTS

Each number in the sequence is the partial sum of A033505 (n starts at 0, each number add one if n is even). We can also find the recursion relation a(n) = 2*a(n-1) + 4*a(n-2) - a(n-4) for the sequence, which could can be proved by induction.

CROSSREFS

Cf. A033505 .

AUTHOR

_Zijing Wu, _, Jul 11 2018

STATUS

proposed

editing

Discussion

Sat Jul 14

14:25

Jon E. Schoenfield: @Zijing Wu:  I undid your incorrect edit to the Author field.