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Search: id:A092876
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| A092876 |
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Coefficients of a solution to a functional equation. |
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+0
1
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| 1, -1, 1, -2, 1, 0, 1, 1, -1, -2, 0, 0, 2, 2, -3, 2, -6, 3, 1, 2, 2, -2, -4, 0, -2, 5, 7, -8, 6, -16, 7, 1, 6, 6, -7, -10, 1, -2, 11, 14, -17, 12, -34, 16, 3, 12, 11, -12, -22, 1, -6, 24, 30, -36, 25, -70, 32, 6, 25, 24, -26, -42, 2, -10, 45, 56, -68, 48, -132, 60, 12, 45, 43, -46, -78, 4, -22, 84, 106, -126, 89, -242, 110, 20, 84, 80
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Euler transform of period 13 sequence [ -1,1,-1,-1,1,1,1,1,-1,-1,1,-1,0,...].
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FORMULA
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G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)=u^2-v+u*v^3+u^3*v^2+2*u*v*(1-u+v+u*v).
G.f. A(x) satisfies 0=f(A(x), A(x^3)) where f(u, v)=u^3*v*(3+3*v+v^2) +3*u^2*v*(v^2+v-1) +u*v*(1-3*v+3*v^2) -(u^4+v^4)
G.f.: x Product_{k>0} (1-x^k)^kronecker(13, k).
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PROGRAM
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(PARI) {a(n)=if(n<1, 0, n--; polcoeff( prod(k=1, n, (1-x^k)^kronecker(13, k), 1+x*O(x^n)), n))} /* Michael Somos Oct 24 2005 */
(PARI) {a(n)=local(A, u, v); if(n<0, 0, A=x; for(k=2, n, u=A+x*O(x^k); v=subst(u, x, x^2); A-=x^k*polcoeff(u^2-v+u*v^3+u^3*v^2+2*u*v*(1-u+v+u*v), k+1)/2); polcoeff(A, n))}
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CROSSREFS
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Sequence in context: A130654 A053259 A143842 this_sequence A024940 A054635 A003137
Adjacent sequences: A092873 A092874 A092875 this_sequence A092877 A092878 A092879
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Mar 09 2004
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