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A034999 Number of ways to cut a 2 X n rectangle into rectangles with integer sides. 4
1, 2, 8, 34, 148, 650, 2864, 12634, 55756, 246098, 1086296, 4795090, 21166468, 93433178, 412433792, 1820570506, 8036386492, 35474325410, 156591247016, 691227204226, 3051224496244, 13468756547882, 59453967813584, 262442511046330, 1158477291582892 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is 1, 4, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... . - Philippe Deléham, Dec 10 2011

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (6,-7).

FORMULA

a(n) = 1+3^(n-1) + Sum_{i=1..n-1} (1+3^(i-1)) a(n-i).

a(n) = 6a(n - 1) - 7a(n - 2), a(n) = ((4 + sqrt(2)) (3 + sqrt(2))^n + (4 - sqrt(2)) (3 - sqrt(2))^n)/14. - N. Sato, May 10 2006

G.f.: (1-x)*(1-3*x)/(1-6*x+7*x^2). - Richard Stanley, Dec 09 2011

EXAMPLE

For n=2 the a(2) = 8 ways to cut are:

.___.  .___.  .___.  .___.  .___.  .___.  .___.  .___.

|   |  | | |  |___|  | |_|  |_| |  |___|  |_|_|  |_|_|

|___|  |_|_|  |___|  |_|_|  |_|_|  |_|_|  |___|  |_|_|  .

CROSSREFS

Column 2 of A116694. - Alois P. Heinz, Dec 10 2012

Sequence in context: A014445 A113440 A296227 * A067336 A245090 A151829

Adjacent sequences:  A034996 A034997 A034998 * A035000 A035001 A035002

KEYWORD

nonn,changed

AUTHOR

Erich Friedman

EXTENSIONS

a(0) added by Richard Stanley, Dec 09 2011

STATUS

approved

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Last modified January 22 04:27 EST 2020. Contains 331133 sequences. (Running on oeis4.)