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Search: id:A064817
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| A064817 |
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Maximal number of squares among the n-1 numbers p_i + p_{i+1}, 1 <= i <= n-1, where (p_1, ..., p_n) is any permutation of (1, ..., n). |
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+0
2
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| 0, 0, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 16, 17, 18, 19, 20, 22, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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a(n) < n by definition, but if we counted the sum p_n + p_1, we could get a(n) = n for 32 <= n <= 49 (see A071984). - David Wasserman (wasserma(AT)spawar.navy.mil), Aug 20 2002
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REFERENCES
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Bernardo Recaman Santos, Challenging Brainteasers, Sterling, NY, 2000, page 71, shows a(15) = 14 using 9,7,2,14,11,5,4,12,13,3,6,10,15,1,8.
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EXAMPLE
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n=8: take 2,7,8,1,3,6,4,5 to get 5 squares: 2+7, 8+1, 1+3, 3+6, 4+5; a(8) = 5.
(1,8,9,7,2,14,11,5,4,12,13,3,6,10) gives 12 squares and no permutation of (1..14) gives more, so a(14)=12.
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CROSSREFS
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Cf. A035106, A064764, A064796, A064797, A071983, A071984.
Sequence in context: A053433 A091401 A091402 this_sequence A108549 A045779 A062014
Adjacent sequences: A064814 A064815 A064816 this_sequence A064818 A064819 A064820
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KEYWORD
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nonn,nice,more
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 23 2001
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 23 2001
More terms from John W. Layman and Charles K. Layman (layman(AT)math.vt.edu; cklayman(AT)juno.com), Nov 07 2001
More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Aug 20 2002
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