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A330130
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Number of length-n binary words having no even palindromes of length > 2 and no odd palindromes of length > 5.
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1
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1, 2, 4, 8, 12, 18, 26, 28, 30, 32, 34, 36, 40, 44, 48, 52, 56, 60, 64, 68, 74, 80, 88, 96, 104, 112, 120, 128, 138, 148, 162, 176, 192, 208, 224, 240, 258, 276, 300, 324, 354, 384, 416, 448, 482, 516, 558, 600, 654, 708, 770, 832, 898, 964, 1040, 1116, 1212
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1,0,1).
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FORMULA
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a(n) = a(n - 8)+a(n - 10) for n >= 16.
Furthermore, a(n) ~ C1*alpha^n +C2*(-alpha)^n, C1 ~ 15.991809, C2 ~ 0.023895, and α ~ 1.0804184273981 is the largest real zero of X^10 - X^2 -1.
G.f.: (1 + 2*x + 4*x^2 + 8*x^3 + 12*x^4 + 18*x^5 + 26*x^6 + 28*x^7 + 29*x^8 + 30*x^9 + 29*x^10 + 26*x^11 + 24*x^12 + 18*x^13 + 10*x^14 + 6*x^15) / (1 - x^8 - x^10). - Colin Barker, Dec 02 2019
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1, 0, 1}, {1, 2, 4, 8, 12, 18, 26, 28, 30, 32, 34, 36, 40, 44, 48, 52}, 60] (* Harvey P. Dale, Oct 15 2021 *)
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PROG
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(PARI) Vec((1 + 2*x + 4*x^2 + 8*x^3 + 12*x^4 + 18*x^5 + 26*x^6 + 28*x^7 + 29*x^8 + 30*x^9 + 29*x^10 + 26*x^11 + 24*x^12 + 18*x^13 + 10*x^14 + 6*x^15) / (1 - x^8 - x^10) + O(x^60)) \\ Colin Barker, Dec 02 2019
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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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