A106219 - OEIS

A106219

Self-convolution cube-root of A106216, which consists entirely of digits {0,1,2} after the initial terms {1,3}.

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

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..31.

FORMULA

Limit a(n+1)/a(n) = -3.09744345956297443415996844224370585278444314...

EXAMPLE

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,...}.

PROG

(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)))}

CROSSREFS

Cf. A106216, A106217, A106218.

Sequence in context: A289666 A084261 A063026 * A198304 A032129 A304914

Adjacent sequences: A106216 A106217 A106218 * A106220 A106221 A106222

KEYWORD

sign

AUTHOR

Paul D. Hanna, May 01 2005

STATUS

approved