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Search: id:A136289
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| A136289 |
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Start with three pennies touching each other on a table-top, and in each generation add pennies subject to the rule that a penny can be placed only when (at least) two pennies are already in position to determine its position; sequence gives number of pennies added at generation n. |
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+0
2
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| 3, 3, 6, 9, 9, 12, 15, 15, 18, 21, 21, 24, 27, 27, 30, 33, 33, 36, 39, 39, 42, 45, 45, 48, 51, 51, 54, 57, 57, 60, 63, 63, 66, 69, 69, 72, 75, 75, 78, 81, 81, 84, 87, 87, 90, 93, 93, 96, 99, 99, 102, 105, 105, 108, 111, 111, 114, 117, 117, 120, 123, 123, 126, 129, 129, 132
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Is there a recurrence or generating function?
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FORMULA
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Conjecture: a(n)=a(n-3)+6, implying g.f.=3*(1+x^2)/((-1+x)^2*(1+x+x^2)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 15 2008
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EXAMPLE
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After four generations we have:
.............4...3...4............
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.......4...3...2...2...3...4......
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.........3...1...0...1...3........
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.......4...2...0...0...2...4......
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.........3...2...1...2...3........
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...........4...3...3...4..........
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.................4................
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MAPLE
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isAdjac := proc(a, b, c) abs(b-a) = 1 and abs(c-b)=1 and abs(a-c)=1 ; end: neighbrs := proc(x) local y, phi ; y := {} ; for phi from 0 to 5 do y := y union {x+expand(exp(I*phi*Pi/3)) } ; od: end: doesMatch2 := proc(genLin, x) local p ; for p in combinat[choose](genLin, 2) do if isAdjac(x, op(1, p), op(2, p)) then RETURN(true) ; fi ; od: RETURN(false) ; end: A136289 := proc(gen) local newgen, o, candid, x, genLin, g ; newgen := {}; genLin := {} ; for g in gen do genLin := genLin union g ; od: for o in op(-1, gen) do candid := neighbrs(o) ; for x in candid do if not x in newgen then if not x in genLin then if doesMatch2(genLin, x) then newgen := newgen union {x} ; fi ; fi ; fi ; od: od: RETURN( [op(gen), newgen] ) ; end: gen := [{0, 1, expand(exp(I*Pi/3))}] : for n from 1 do printf("%d, ", nops(op(n, gen)) ) ; gen := A136289(gen) od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 15 2008
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CROSSREFS
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Cf. A136290.
Adjacent sequences: A136286 A136287 A136288 this_sequence A136290 A136291 A136292
Sequence in context: A110769 A093445 A098358 this_sequence A128012 A058628 A035528
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KEYWORD
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nonn
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AUTHOR
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Colin Mallows (colinm(AT)research.avayalabs.com), Apr 13 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 15 2008
More terms from John W. Layman (layman(AT)math.vt.edu), Jun 26 2008
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