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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
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
Sequence in context: A019479 A084814 A098125 * A296399 A119471 A145779
KEYWORD
nonn,easy
AUTHOR
Michael Tulskikh, May 30 2020
STATUS
approved

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Last modified June 20 16:01 EDT 2024. Contains 373526 sequences. (Running on oeis4.)