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A330130 Number of length-n binary words having no even palindromes of length > 2 and no odd palindromes of length > 5. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Lukas Fleischer, Jeffrey Shallit, Words With Few Palindromes, Revisited, arxiv preprint arXiv:1911.12464 [cs.FL], November 27 2019.
FORMULA
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
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A080476 A256885 A293495 * A053799 A343949 A284122
KEYWORD
nonn,easy
AUTHOR
Jeffrey Shallit, Dec 02 2019
STATUS
approved

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Last modified March 29 06:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)