A112573 G.f. A(x) satisfies: A(x)^3 equals the g.f. of A110640, which consists entirely of numbers 1 through 9.

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

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: A368554 A301477 A261895 * A233740 A266595 A120406

Adjacent sequences: A112570 A112571 A112572 * A112574 A112575 A112576

Keyword

sign

Author

Paul D. Hanna, Sep 14 2005

Status

approved