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A112573 G.f. A(x) satisfies: A(x)^3 equals the g.f. of A110640, which consists entirely of numbers 1 through 9. 0
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; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A110640 is formed from every third term of A083949, which also consists entirely of numbers 1 through 9.

LINKS

Table of n, a(n) for n=0..37.

FORMULA

G.f. A(x) satisfies: A(x)^9 (mod 27) = g.f. of A083949.

EXAMPLE

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.

PROG

(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)}

CROSSREFS

Cf. A110640, A083949.

Sequence in context: A250303 A301477 A261895 * A233740 A266595 A120406

Adjacent sequences:  A112570 A112571 A112572 * A112574 A112575 A112576

KEYWORD

sign

AUTHOR

Paul D. Hanna, Sep 14 2005

STATUS

approved

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Last modified October 22 07:06 EDT 2021. Contains 348160 sequences. (Running on oeis4.)