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A221174
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a(0)=-4, a(1)=5; thereafter a(n) = 2*a(n-1) + a(n-2).
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7
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-4, 5, 6, 17, 40, 97, 234, 565, 1364, 3293, 7950, 19193, 46336, 111865, 270066, 651997, 1574060, 3800117, 9174294, 22148705, 53471704, 129092113, 311655930, 752403973, 1816463876, 4385331725, 10587127326, 25559586377, 61706300080, 148972186537, 359650673154
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OFFSET
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0,1
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COMMENTS
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For n >= 3, 2*a(n) is the number of ways to tile this figure of length n-1 with two colors of squares and one color of domino. For n=8, we have here the figure of length n-1=7, and it has 2*a(8) = 2728 different tilings.
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(End)
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LINKS
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FORMULA
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a(n) is the numerator of the continued fraction [4, 2, ..., 2, 4] with n-3 2's in the middle. For denominators, see A048654. - Greg Dresden and Tongjia Rao, Sep 02 2021
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PROG
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(Haskell)
a221174 n = a221174_list !! n
a221174_list = -4 : 5 : zipWith (+)
(map (* 2) $ tail a221174_list) a221174_list
(PARI) Vec(-(13*x-4)/(x^2+2*x-1) + O(x^50)) \\ Colin Barker, Jul 10 2015
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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