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A100538
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Volume of the 3-dimensional box of sides of length equal to consecutive Padovan numbers (A000931). These boxes form a spiral in three dimensions similar to the spiral of fibonacci boxes in two dimensions.
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0
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1, 2, 4, 12, 24, 60, 140, 315, 756, 1728, 4032, 9408, 21756, 50764, 117845, 273910, 637260, 1480404, 3442800, 8003000, 18603000, 43251975, 100540440, 233735040, 543371136, 1263161472, 2936540824, 6826574552, 15869878969, 36893076570
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..30.
I. Stewart, Tales of a Neglected Number
Index to sequences with linear recurrences with constant coefficients, signature (1,2,3,-2,4,-4,-1,-1,0,-1). [From R. J. Mathar, Sep 14 2010]
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FORMULA
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For large n a(n+1) -> a(n) * p^3 where p is the plastic number = 1.324718... a(n+1) = a(n)+ (a(n)/P(n))*P(n+1 ) where P are the Padovan numbers (A000931) starting 1, 1, 1, 2, 2, 3, 4, 5, 7 etc
a(n)= +a(n-1) +2*a(n-2) +3*a(n-3) -2*a(n-4) +4*a(n-5) -4*a(n-6) -a(n-7) -a(n-8) -a(n-10) = A000931(n+4)*A000931(n+5)*A000931(n+6). G.f.: x*(1+x+x^3) / ( (x-1)*(x^3-2*x^2+3*x-1)*(x^6+3*x^5+5*x^4+5*x^3+5*x^2+3*x+1) ). [From R. J. Mathar, Sep 14 2010]
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CROSSREFS
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Sequence in context: A045687 A057422 A036045 * A135139 A161894 A062177
Adjacent sequences: A100535 A100536 A100537 * A100539 A100540 A100541
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KEYWORD
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nonn
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AUTHOR
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John Lien, Nov 27 2004
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EXTENSIONS
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More terms from R. J. Mathar, Sep 14 2010
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STATUS
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approved
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