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A136429
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a(n) = Sum_{k=0..n} F(k+1)^2*F(n-k+1)^2 where F = Fibonacci numbers (A000045).
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1
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1, 2, 9, 26, 84, 250, 747, 2182, 6323, 18132, 51624, 146004, 410677, 1149578, 3204477, 8899502, 24634620, 67990414, 187154271, 513939214, 1408246247, 3851081256, 10512259920, 28647203880, 77946605545, 211782868754
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of ways to tile a 2 X (n+1) board with squares and dominoes with exactly one vertical domino. - Greg Dresden and Zijie He, Jun 14 2022
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LINKS
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FORMULA
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G.f.: (1-x)^2/((1+x)^2*(1-3x+x^2)^2).
Recurrence: a(n+6) = 4a(n+5) - 10a(n+3) + 4a(n+1) - a(n).
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PROG
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(PARI) a(n) = sum(k=0, n, fibonacci(k+1)^2*fibonacci(n-k+1)^2); \\ Michel Marcus, Jan 13 2021
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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