A332491
a(n) = 2*a(n-1) + a(n-3), where a(0) = 3, a(1) = 1, a(2) = 2.
Original entry on oeis.org
3, 1, 2, 7, 15, 32, 71, 157, 346, 763, 1683, 3712, 8187, 18057, 39826, 87839, 193735, 427296, 942431, 2078597, 4584490, 10111411, 22301419, 49187328, 108486067, 239273553, 527734434, 1163954935, 2567183423, 5662101280, 12488157495, 27543498413
Offset: 0
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LinearRecurrence[{2,0,1},{3,1,2},40] (* Harvey P. Dale, Apr 20 2025 *)
A345448
Number of tilings of a 2 X n rectangle with dominoes and long L-shaped 4-minoes.
Original entry on oeis.org
1, 1, 2, 7, 15, 32, 79, 185, 422, 987, 2307, 5352, 12451, 29005, 67478, 156991, 365391, 850304, 1978615, 4604465, 10715078, 24934611, 58024779, 135028632, 314222011, 731218981, 1701605078, 3959769367, 9214694391, 21443322032, 49900304047, 116121942377
Offset: 0
For n = 3 the a(3)=7 tilings are:
._____. ._____. ._____. ._____.
| |___| |___| | | ___| |___ |
|_____| |_____| |_|___| |___|_|
._____. ._____. ._____.
|___| | | |___| | | | |
|___|_| |_|___| |_|_|_|
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LinearRecurrence[{1, 1, 4, 2}, {1, 1, 2, 7}, 40]
A387619
Number of ways to tile a 2 X n strip with squares, dominoes, and (straight and bent) trominoes.
Original entry on oeis.org
1, 2, 11, 51, 235, 1092, 5064, 23489, 108954, 505377, 2344171, 10873339, 50435526, 233943074, 1085135139, 5033353844, 23347000765, 108294084141, 502317568673, 2329978980834, 10807509809918, 50130181109907, 232526743191648, 1078565548781339, 5002881075314417
Offset: 0
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LinearRecurrence[{3, 6, 7, 2, 0, -1}, {1, 2, 11, 51, 235, 1092}, 40]
Comments