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A335274 a(n) = 2*a(n-1) + a(n-3), where a(0) = 0, a(1) = 1, a(2) = 4. 1
0, 1, 4, 8, 17, 38, 84, 185, 408, 900, 1985, 4378, 9656, 21297, 46972, 103600, 228497, 503966, 1111532, 2451561, 5407088, 11925708, 26302977, 58013042, 127951792, 282206561, 622426164, 1372804120, 3027814801, 6678055766 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is the number of ways to tile a 2 x n strip, with a bent tromino added to the top, with dominos and L-shaped trominos:

._

|_|_

|_|_|_ _ _

|_|_|_|_|_| . . .

|_|_|_|_|_| . . .

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,1).

FORMULA

a(n) = 2*a(n-1) + a(n-3).

a(n) = 2*A008998(n-1) - A008998(n-4).

a(n) = A008998(n-1) + 2*A008998(n-2).

G.f.: x*(1 + 2*x) / (1 - 2*x - x^3). - Colin Barker, Jun 04 2020

EXAMPLE

a(2) = 4 as shown by these four tilings:

._         _         _         _

|X|_      | |_      |X|_      | |_

|X|X|  ,  |_|X|  ,  |X|X|  ,  |_| |

|_ _|     |X X|     | | |     |X|_|

|_ _|     |_ _|     |_|_|     |X X|

PROG

(PARI) concat(0, Vec(x*(1 + 2*x) / (1 - 2*x - x^3) + O(x^35))) \\ Colin Barker, Jun 04 2020

CROSSREFS

Cf. A008998, A335242.

Sequence in context: A019479 A084814 A098125 * A296399 A119471 A145779

Adjacent sequences:  A335271 A335272 A335273 * A335275 A335276 A335277

KEYWORD

nonn,easy

AUTHOR

Michael Tulskikh, May 30 2020

STATUS

approved

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Last modified May 22 20:08 EDT 2022. Contains 353957 sequences. (Running on oeis4.)