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Search: id:A112573
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| A112573 |
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G.f. A(x) satisfies: A(x)^3 equals the g.f. of A110640, which consists entirely of numbers 1 through 9. |
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1
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| 1, 1, 0, 0, 2, -2, 5, -6, 5, 3, -26, 70, -141, 221, -229, -18, 891, -2914, 6524, -11238, 13690, -4214, -37619, 145018, -353534, 657080, -895234, 534007, 1654246, -7840402, 20737566, -41200153, 61402057, -50500722, -68352913, 441195837, -1272153666, 2690651374
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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A110640 is formed from every third term of A083949, which also consists entirely of numbers 1 through 9.
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FORMULA
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G.f. A(x) satisfies: A(x)^9 (mod 27) = g.f. of A083949.
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EXAMPLE
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A(x) = 1 + x + 2*x^4 - 2*x^5 + 5*x^6 - 6*x^7 + 5*x^8 + 3*x^9 +...
A(x)^3 = 1 + 3*x + 3*x^2 + x^3 + 6*x^4 + 6*x^5 + 9*x^6 + 6*x^7 +...
A(x)^9 = 1 + 9*x + 36*x^2 + 84*x^3 + 144*x^4 + 252*x^5 + 489*x^6 +..
A(x)^9 (mod 27) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 + 3*x^6+..
G(x) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 + 3*x^6 + 9*x^7 +...
where G(x) is the g.f. of A083949.
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PROGRAM
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(PARI) {a(n)=local(d=3, m=9, A=1+m*x); for(j=2, d*n, for(k=1, m, t=polcoeff((A+k*x^j+x*O(x^j))^(1/m), j); if(denominator(t)==1, A=A+k*x^j; break))); polcoeff(Ser(vector(n+1, i, polcoeff(A, d*(i-1))))^(1/3), n)}
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CROSSREFS
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Cf. A110640, A083949.
Sequence in context: A103892 A000403 A068763 this_sequence A120406 A050157 A054255
Adjacent sequences: A112570 A112571 A112572 this_sequence A112574 A112575 A112576
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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), Sep 14 2005
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