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A366143 a(n) = a(n-2) + 2*a(n-4) - a(n-10), with a[0..9] = [1, 1, 1, 1, 1, 2, 3, 5, 6, 9]. 1
1, 1, 1, 1, 1, 2, 3, 5, 6, 9, 11, 18, 22, 35, 43, 69, 84, 134, 164, 263, 321, 513, 627, 1004, 1226, 1961, 2396, 3835, 4684, 7494, 9155, 14651, 17896, 28635, 34980, 55976, 68376, 109411, 133652, 213869, 261249, 418040, 510657, 817143, 998175, 1597247, 1951113 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
a(n) is the number of ways to tile a zig-zag strip of n cells using squares (of 1 cell) and strips (of 3 cells). Here is the zig-zag strip corresponding to n=11, with 11 cells:
___ ___
___| |___| |___
| |___| |___| |___
|___| |___| |___| |
| |___| |___| |___|
|___| |___| |___|,
and here is the strip of 3 cells (which can be reflected)
___
___| |
___| ___|
| ___|
|___|
As an example, here is one of the a(11) = 18 ways to tile the zig-zag strip of 11 cells:
___ ___
___| |___| |___
| |___| |___ |___
|___| ___| |___ |
| ___| |___| |___|
|___| |___| |___|
LINKS
FORMULA
a(n) = a(n-2) + 2*a(n-4) - a(n-10).
a(2*n) = a(2*n-1) + a(2*n-4) - a(2*n-5) + a(2*n-6).
a(2*n+1) = a(2*n) + 2*a(2*n-3) - a(2*n-4) + a(2*n-6) - a(2*n-7).
G.f.: (x^8+x^7-x^5-2*x^4+x+1)/(x^10-2*x^4-x^2+1).
MATHEMATICA
LinearRecurrence[{0, 1, 0, 2, 0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 1, 2,
3, 5, 6, 9}, 40]
CROSSREFS
Cf. A135318.
Sequence in context: A241819 A227070 A032718 * A086191 A074658 A186106
KEYWORD
nonn,easy
AUTHOR
Greg Dresden and Ziyi Xie, Sep 30 2023
STATUS
approved

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Last modified July 13 23:31 EDT 2024. Contains 374290 sequences. (Running on oeis4.)