OFFSET
0,5
COMMENTS
a(n) is also the number of ways to tile a strip of length n with squares, dominoes, and tetrominoes such that the first tile is NOT a square. As such, it completes the set of such tilings with A005251 (first tile is NOT a domino), A005314 (first tile is NOT a tetromino), and A060945 (no restrictions on first tile).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..4096
Jean-Luc Baril, Sergey Kirgizov, and Armen Petrossian, Dyck Paths with catastrophes modulo the positions of a given pattern, Australasian J. Comb. (2022) Vol. 84, No. 2, 398-418.
Index entries for linear recurrences with constant coefficients, signature (1,1,0,1).
FORMULA
MATHEMATICA
CoefficientList[Series[(1 - x)/(1 - x - x^2 - x^4), {x, 0, 40}], x] (* Michael De Vlieger, Mar 04 2022 *)
LinearRecurrence[{1, 1, 0, 1}, {1, 0, 1, 1}, 60] (* Harvey P. Dale, Aug 17 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Greg Dresden and Yichen P. Wang, Sep 03 2021
STATUS
approved