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A347493
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a(0) = 1, a(1) = 0, a(2) = a(3) = 1; thereafter, a(n) = a(n-1) + a(n-2) + a(n-4).
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1
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1, 0, 1, 1, 3, 4, 8, 13, 24, 41, 73, 127, 224, 392, 689, 1208, 2121, 3721, 6531, 11460, 20112, 35293, 61936, 108689, 190737, 334719, 587392, 1030800, 1808929, 3174448, 5570769, 9776017, 17155715, 30106180, 52832664, 92714861, 162703240, 285524281, 501060185, 879299327, 1543062752
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OFFSET
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0,5
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COMMENTS
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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).
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LINKS
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FORMULA
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G.f.: (1 - x)/(1 - x - x^2 - x^4).
Sum_{k=0..n} a(k)*F(n-k) = a(n+3) - F(n+2) for F(n)=A000045(n) the Fibonacci numbers.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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