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Search: id:A106219
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| A106219 |
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Self-convolution cube-root of A106216, which consists entirely of digits {0,1,2} after the initial terms {1,3}. |
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+0
8
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| 1, 1, -1, 2, -4, 9, -21, 53, -137, 362, -971, 2642, -7272, 20211, -56631, 159795, -453650, 1294797, -3713100, 10693036, -30910440, 89657680, -260860962, 761114168, -2226409022, 6528039545, -19182376302, 56479676608, -166605140314, 492304708589, -1457061274821, 4318906269671
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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Limit a(n+1)/a(n) = -3.09744345956297443415996844224370585278444314...
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EXAMPLE
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A(x) = 1 + x - x^2 + 2*x^3 - 4*x^4 + 9*x^5 - 21*x^6 + 53*x^7 -+...
A(x)^3 = 1 + 3*x + x^3 + 2*x^6 + 2*x^9 + 2*x^12 + 2*x^21 + x^24 +...
A106216 = {1,3,0,1,0,0,2,0,0,2,0,0,2,0,0,0,0,0,0,0,0,2,0,0,1,...}.
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PROGRAM
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(PARI) {a(n)=local(A=1+3*x); if(n==0, 1, for(j=1, n, for(k=0, 2, t=polcoeff((A+k*x^j+x*O(x^j))^(1/3), j); if(denominator(t)==1, A=A+k*x^j; break))); return(polcoeff((A+x*O(x^n))^(1/3), n)))}
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CROSSREFS
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Cf. A106216, A106217, A106218.
Sequence in context: A136753 A084261 A063026 this_sequence A032129 A005217 A148072
Adjacent sequences: A106216 A106217 A106218 this_sequence A106220 A106221 A106222
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 01 2005
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