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Search: id:A107087
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| A107087 |
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G.f. A(x) satisfies: A(x)^2 = A(x^2) + 4*x. |
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+0
3
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| 1, 2, -1, 2, -5, 12, -30, 82, -233, 668, -1949, 5802, -17503, 53302, -163783, 507418, -1582869, 4966790, -15667573, 49658264, -158059506, 505013014, -1619144976, 5207596574, -16797286048, 54323516786, -176113786590, 572236347200, -1863213388504, 6078422747600, -19865661574555
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Self-convolution of A107086. Self-convolution yields A107088.
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FORMULA
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G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=u^4+4*w-2*u^2*v-3*v^2 . - Michael Somos May 15 2005
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EXAMPLE
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A(x)^2 = 1 + 4*x + 2*x^2 - x^4 + 2*x^6 - 5*x^8 + 12*x^10 - 30*x^12 +...
A(x^2) = 1 + 2*x^2 - x^4 + 2*x^6 - 5*x^8 + 12*x^10 - 30*x^12 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=(subst(A, x, x^2)+4*x+x*O(x^n))^(1/2)); polcoeff(A, n, x)}
(PARI) {a(n)=local(m, A); if(n<0, 0, A=1+O(x); m=1; while(m<=n, A=sqrt(4*x+subst(A, x, x^2)); m*=2); polcoeff(A, n))} /* Michael Somos May 15 2005 */
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CROSSREFS
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Cf. A107086, A107088.
Sequence in context: A049901 A117715 A160457 this_sequence A115141 A031148 A032238
Adjacent sequences: A107084 A107085 A107086 this_sequence A107088 A107089 A107090
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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 11 2005
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