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Search: id:A143926
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| A143926 |
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G.f. satisfies: A(x) = 1 + x*A(x)*A(-x) + x^2*A(x)^2*A(-x)^2. |
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+0
2
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| 1, 1, 1, 1, 2, 3, 7, 11, 28, 46, 123, 207, 572, 979, 2769, 4797, 13806, 24138, 70414, 123998, 365636, 647615, 1926505, 3428493, 10273870, 18356714, 55349155, 99229015, 300783420, 540807165, 1646828655, 2968468275, 9075674700
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Bisections form A006605 and A143927;
A006605 is the number of modes of connections of 2n points and
A143927 is the self-convolution of A006605.
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FORMULA
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Define B(x) by B(x^2) = A(x)*A(-x); then B(x) = 1 + x*B(x)^2 + x^2*B(x)^4 is the g.f. of A006605.
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EXAMPLE
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G.f. A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 7*x^6 + 11*x^7 +...
A(x)*A(-x) = 1 + x^2 + 3*x^4 + 11*x^6 + 46*x^8 + 207*x^10 + 979*x^12 +...
A(x)^2*A(-x)^2 = 1 + 2*x^2 + 7*x^4 + 28*x^6 + 123*x^8 + 572*x^10 +...
A(x)^4*A(-x)^4 = 1 + 4*x^2 + 18*x^4 + 84*x^6 + 407*x^8 + 2028*x^10 +...
from this we see that if B(x^2) = A(x)*A(-x)
then B(x) = 1 + x*B(x)^2 + x^2*B(x)^4
and A(x) = 1 + x*B(x^2) + x^2*B(x^2)^2.
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PROGRAM
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, B=A*subst(A, x, -x); A=1+x*B+x^2*B^2); polcoeff(A, n)}
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CROSSREFS
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Cf. A006605, A143927.
Sequence in context: A095055 A107857 A107858 this_sequence A112840 A014981 A096362
Adjacent sequences: A143923 A143924 A143925 this_sequence A143927 A143928 A143929
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Sep 06 2008
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