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A292764
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Minimal number of moves for the cyclic variant of Hanoi's tower for 4 pegs and n disks, with the final peg two steps away.
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5
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2, 8, 18, 36, 66, 120, 210, 360, 618, 1052, 1790, 3040, 5162, 8756, 14854, 25192, 42722, 72444, 122846, 208304, 353210
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..21.
Paul K. Stockmeyer, Variations on the Four-Post Tower of Hanoi Puzzle, Congressus Numerantium 102 (1994), pp. 3-12;
Paul Zimmermann, Sage program
Index entries for sequences related to Towers of Hanoi
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FORMULA
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Conjecture: for n >= 9, a(n) = a(n-1)+2*a(n-3)+c(n), where c(n) = 18 for odd n and c(n) = 14 for even n. - Paul Zimmermann, Oct 23 2017
Conjectures from Colin Barker, Oct 25 2017: (Start)
G.f.: 2*x*(1 + 3*x + 4*x^2 + 4*x^3 + 2*x^4 + 2*x^5 + 2*x^6 - 2*x^9) / ((1 - x)*(1 + x)*(1 - x - 2*x^3)).
a(n) = a(n-1) + a(n-2) + a(n-3) -2*a(n-5) for n>10. [corrected by Paul Zimmermann, Oct 07 2020
(End)
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CROSSREFS
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Cf. A292765.
Sequence in context: A018229 A166830 A072779 * A198014 A252592 A188577
Adjacent sequences: A292761 A292762 A292763 * A292765 A292766 A292767
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KEYWORD
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nonn,more
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AUTHOR
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N. J. A. Sloane, Sep 27 2017, following a suggestion from Paul Zimmermann who computed the terms through a(16).
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EXTENSIONS
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Extended through a(21) by Paul Zimmermann, Oct 23 2017
Name clarified by Paul Zimmermann, Oct 29 2017
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STATUS
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approved
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