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A356807
Tetranacci sequence beginning with 3, 7, 12, 24.
1
3, 7, 12, 24, 46, 89, 171, 330, 636, 1226, 2363, 4555, 8780, 16924, 32622, 62881, 121207, 233634, 450344, 868066, 1673251, 3225295, 6216956, 11983568, 23099070, 44524889, 85824483, 165432010, 318880452, 614661834, 1184798779, 2283773075, 4402114140, 8485347828
OFFSET
1,1
COMMENTS
By "Tetranacci sequence" we mean a sequence in which each term is the sum of the four previous terms.
For n>1, a(n) is the number of ways to tile this figure of length n with squares, dominoes, trominoes, and tetraminoes:
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FORMULA
a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4).
a(n) = 5*b(n+2) + 2*b(n+1) - 2*b(n-2) for b(n) = A000078(n) the tetranacci numbers.
a(n) = L(n+2) - F(n-2) + Sum_{k=0..n-3} a(k)*F(n-k-1), for L(n) and F(n) the Lucas and Fibonacci numbers.
G.f.: x*(-2*x^3 - 2*x^2 - 4*x - 3)/(x^4 + x^3 + x^2 + x - 1). - Chai Wah Wu, Aug 30 2022
EXAMPLE
Here is one of the a(6) = 89 ways to tile this figure of length 6 with tiles of length <= 4, this one using three squares, one domino, and one tromino:
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MATHEMATICA
LinearRecurrence[{1, 1, 1, 1}, {3, 7, 12, 24}, 50] (* Paolo Xausa, Aug 30 2024 *)
CROSSREFS
Sequence in context: A262567 A226229 A167491 * A210185 A280345 A062325
KEYWORD
nonn,easy
AUTHOR
Greg Dresden and Hangyu Liang, Aug 29 2022
STATUS
approved