A112123 -id:A112123 - cp's OEIS frontend

A112122 Unique sequence of numbers {1,2,3,...,11} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (11th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 10, 11, 11, 11, 11, 11, 11, 11, 11, 10, 2, 7, 1, 1, 1, 1, 1, 1, 1, 11, 1, 10, 1, 3, 3, 3, 3, 3, 3, 2, 2, 10, 11, 11, 3, 3, 3, 3, 3, 2, 6, 9, 5, 3, 2, 4, 4, 4, 4, 3, 5, 11, 6, 7

Offset: 1

Paul D. Hanna, Aug 27 2005

nonn

			G.f.: A(x) = x + 11*x^2 + 11*x^3 + 11*x^4 + 11*x^5 +...
then A(x) = B(B(B(B(B(B(B(B(B(B(B(x))))))))))) where
B(x) = x + x^2 - 9*x^3 + 131*x^4 - 2279*x^5 + 43161*x^6 +...
is the g.f. of A112123.

Cf. A112123, A112104-A112121, A112124-A112127.

{a(n,m=11)=local(F=x+x^2+x*O(x^n),G);if(n<1,0, for(k=3,n, G=F+x*O(x^k);for(i=1,m-1,G=subst(F,x,G)); F=F-((polcoeff(G,k)-1)\m)*x^k); G=F+x*O(x^n);for(i=1,m-1,G=subst(F,x,G)); return(polcoeff(G,n,x)))}

A112124 Unique sequence of numbers {1,2,3,...,12} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (12th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

Original entry on oeis.org

1, 12, 12, 6, 8, 8, 12, 2, 8, 2, 10, 9, 10, 10, 4, 5, 4, 7, 10, 10, 12, 7, 12, 8, 8, 9, 10, 7, 11, 12, 2, 9, 12, 10, 11, 7, 6, 5, 4, 5, 10, 7, 9, 1, 9, 5, 12, 12, 2, 10, 6, 9, 9, 6, 2, 1, 9, 3, 7, 10, 4, 11, 10, 3, 6, 10, 6, 10, 12, 11, 8, 1, 2, 4, 7, 2, 8, 6, 9, 12, 8, 2, 3, 2, 4, 3, 6, 12, 6, 11, 4

Offset: 1

Paul D. Hanna, Aug 27 2005

nonn

			G.f.: A(x) = x + 12*x^2 + 12*x^3 + 6*x^4 + 8*x^5 + 8*x^6 +...
then A(x) = B(B(B(B(B(B(B(B(B(B(B(B(x)))))))))))) where
B(x) = x + x^2 - 10*x^3 + 160*x^4 - 3061*x^5 + 63775*x^6 +...
is the g.f. of A112125.

Cf. A112125, A112104-A112123, A112126, A112127.

{a(n,m=12)=local(F=x+x^2+x*O(x^n),G);if(n<1,0, for(k=3,n, G=F+x*O(x^k);for(i=1,m-1,G=subst(F,x,G)); F=F-((polcoeff(G,k)-1)\m)*x^k); G=F+x*O(x^n);for(i=1,m-1,G=subst(F,x,G)); return(polcoeff(G,n,x)))}

A112125 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (12th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,12}, with B(0) = 0.

Original entry on oeis.org

1, 1, -10, 160, -3061, 63775, -1381434, 30233546, -654989371, 13821523157, -280493565375, 5432981693533, -100769609590332, 1833421110751790, -34286913831217395, 678578947805323394, -13377225136748683778, 221000164094797572734, -2119677884300620846621

Offset: 1

Paul D. Hanna, Aug 27 2005

sign

			A(x) = x + x^2 - 10*x^3 + 160*x^4 - 3061*x^5 + 63775*x^6 +...
where A(A(A(A(A(A(A(A(A(A(A(A(x)))))))))))) =
x + 12*x^2 + 12*x^3 + 6*x^4 + 8*x^5 + 8*x^6 + 12*x^7 + 2*x^8 +...
is the g.f. of A112124.

Cf. A112124, A112104-A112123, A112126, A112127.

{a(n,m=12)=local(F=x+x^2+x*O(x^n),G);if(n<1,0, for(k=3,n, G=F+x*O(x^k);for(i=1,m-1,G=subst(F,x,G)); F=F-((polcoeff(G,k)-1)\m)*x^k); return(polcoeff(F,n,x)))}

cp's OEIS Frontend

A112122 Unique sequence of numbers {1,2,3,...,11} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (11th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

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A112124 Unique sequence of numbers {1,2,3,...,12} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (12th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

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A112125 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (12th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,12}, with B(0) = 0.

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