A354080 -id:A354080 - cp's OEIS frontend

A385717 a(n) = a(n-1) + a(n-2) + a(n-3), with a(1) = 4, a(2) = 13, a(3) = 42.

4, 13, 42, 59, 114, 215, 388, 717, 1320, 2425, 4462, 8207, 15094, 27763, 51064, 93921, 172748, 317733, 584402, 1074883, 1977018, 3636303, 6688204, 12301525, 22626032, 41615761, 76543318, 140785111, 258944190, 476272619

Offset: 1

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Greg Dresden and Jiarui Zhou, Jul 07 2025

nonn
easy

For n >= 3, a(n) is the number of ways to tile this shape of length n with 1 X 1 squares, 1 X 2 dominos, and 1 X 3 trominos:
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As an example, here is one of the a(8) = 717 ways to tile this shape of length 8:
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Index entries for linear recurrences with constant coefficients, signature (1,1,1).

Cf. A100683, A354080.

LinearRecurrence[{1, 1, 1}, {4, 13, 42}, 30]

a(n) = 9*A354080(n-2) + 2*A100683(n) for n >= 2.

G.f.: x*(4 + 9*x + 25*x^2)/(1 - x - x^2 - x^3). - Stefano Spezia, Jul 08 2025

cp's OEIS Frontend

A385717 a(n) = a(n-1) + a(n-2) + a(n-3), with a(1) = 4, a(2) = 13, a(3) = 42.

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