Timeline for Number of ways of tiling a $2 \times n$ rectangle using rectangles with integer sides
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 3, 2016 at 1:25 | comment | added | Robert Israel | i.e. multiply Tony's equation by $x^n$, sum for $n=1 \ldots \infty$ (interchanging the order of summations) and add $1$, and you should get $$g(x) = \dfrac{x}{1-4x} + \dfrac{x g(x)}{1-x} + \dfrac{x^2 g(x)}{1-5x+4x^2}$$ where $g(x)$ is the g.f. Solve: $$ g(x) = \dfrac{1-4x+3x^2}{1-6x+7x^2}$$ | |
| Feb 2, 2016 at 22:17 | comment | added | Robert Israel | You should be able to get the g.f. from Tony Huynh's recursion equation, and it follows from that. | |
| Feb 2, 2016 at 21:53 | comment | added | Gerry Myerson | At OEIS, it says $a_n=6a_{n-1}-7a_{n-2}$. I wonder how one gets that? | |
| Feb 2, 2016 at 16:47 | comment | added | Robert Israel | Sorry, mistake in my program, corrected. Actually you want $f(2,2)=8$. | |
| Feb 2, 2016 at 16:46 | history | undeleted | Robert Israel | ||
| Feb 2, 2016 at 16:46 | history | edited | Robert Israel | CC BY-SA 3.0 |
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| Feb 2, 2016 at 16:41 | history | deleted | Robert Israel | via Vote | |
| Feb 2, 2016 at 16:36 | history | edited | Robert Israel | CC BY-SA 3.0 |
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| Feb 2, 2016 at 16:31 | history | answered | Robert Israel | CC BY-SA 3.0 |