A112127 -id:A112127 - cp's OEIS frontend

A112113 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (6th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,6}, with B(0) = 0.

1, 1, -4, 28, -236, 2159, -20309, 189387, -1696165, 14092143, -103605487, 621674576, -2503235595, 1311059747, 58857366823, -625935119621, 20416246154579, -595556154741631, 9331660766550500, -50486760747953952, -816026626910008666

Offset: 1

Paul D. Hanna, Aug 27 2005

sign

			A(x) = x + x^2 - 4*x^3 + 28*x^4 - 236*x^5 + 2159*x^6 +...
where A(A(A(A(A(A(x)))))) =
x + 6*x^2 + 6*x^3 + 3*x^4 + 4*x^5 + 4*x^6 + 6*x^7 + 2*x^8 +...
is the g.f. of A112112.

Cf. A112112, A112104-A112111, A112114-A112127.

{a(n,m=6)=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)))}

A112114 Unique sequence of numbers {1,2,3,...,7} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (7th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

Original entry on oeis.org

1, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 5, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 7, 4, 7, 4, 4, 4, 3, 2, 5, 3, 1, 1, 7, 5, 2, 4, 2, 2, 1, 2, 6, 5, 1, 5, 7, 7, 7, 7, 5, 6, 5, 6, 4, 1, 6, 1, 2, 7, 1, 5, 3, 7, 2, 4, 4, 4, 3, 2, 4, 5, 7, 7, 3, 1, 2, 3, 5, 5, 6, 4, 7, 6, 1, 6, 5, 2, 1, 1, 6, 1, 4, 3, 1, 2, 3, 3, 3, 7, 1

Offset: 1

Paul D. Hanna, Aug 27 2005

nonn

			G.f.: A(x) = x + 7*x^2 + 7*x^3 + 7*x^4 + 7*x^5 + 7*x^6 + 7*x^7 + ...
then A(x) = B(B(B(B(B(B(B(x))))))) where
B(x) = x + x^2 - 5*x^3 + 43*x^4 - 443*x^5 + 4957*x^6 - 57281*x^7 + ...
is the g.f. of A112115.

Cf. A112115, A112104-A112113, A112116-A112127.

{a(n,m=7)=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)))}

A112115 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (7th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,7}, with B(0) = 0.

Original entry on oeis.org

1, 1, -5, 43, -443, 4957, -57281, 661375, -7430526, 79197417, -778914398, 6845802239, -52074744048, 345158019601, -2374391391323, 20218882229451, -34682204747638, -6385759551091470, 180067413599721613, -2110513020510554883

Offset: 1

Paul D. Hanna, Aug 27 2005

sign

			A(x) = x + x^2 - 5*x^3 + 43*x^4 - 443*x^5 + 4957*x^6 - 57281*x^7 +...
where A(A(A(A(A(A(A(x))))))) =
x + 7*x^2 + 7*x^3 + 7*x^4 + 7*x^5 + 7*x^6 + 7*x^7 +...
is the g.f. of A112114.

Cf. A112114, A112104-A112113, A112116-A112127.

{a(n,m=7)=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)))}

A112116 Unique sequence of numbers {1,2,3,...,8} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (8th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

Original entry on oeis.org

1, 8, 8, 4, 8, 4, 8, 8, 4, 8, 8, 4, 4, 8, 8, 4, 4, 8, 8, 2, 4, 6, 4, 6, 2, 4, 8, 8, 2, 2, 8, 4, 8, 2, 2, 8, 8, 6, 4, 4, 6, 2, 4, 3, 8, 5, 8, 8, 7, 5, 4, 3, 4, 6, 6, 2, 1, 7, 2, 7, 8, 8, 8, 2, 8, 8, 4, 2, 7, 8, 8, 5, 3, 4, 2, 6, 5, 1, 8, 7, 4, 1, 5, 4, 4, 7, 4, 2, 4, 7, 6, 4, 6, 2, 6, 3, 5, 6, 7, 2, 5, 7, 8, 8, 7

Offset: 1

Paul D. Hanna, Aug 27 2005

nonn

			G.f.: A(x) = x + 8*x^2 + 8*x^3 + 4*x^4 + 8*x^5 + 4*x^6 + 8*x^7 +...
then A(x) = B(B(B(B(B(B(B(B(x)))))))) where
B(x) = x + x^2 - 6*x^3 + 60*x^4 - 720*x^5 + 9398*x^6 - 126958*x^7 +...
is the g.f. of A112117.

Cf. A112117, A112104-A112115, A112118-A112127.

{a(n,m=8)=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)))}

A112118 Unique sequence of numbers {1,2,3,...,9} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (9th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

Original entry on oeis.org

1, 9, 9, 9, 6, 6, 3, 9, 6, 3, 9, 3, 3, 1, 7, 5, 9, 1, 8, 6, 2, 6, 4, 6, 7, 6, 4, 6, 3, 2, 5, 7, 2, 5, 7, 8, 1, 4, 9, 6, 3, 7, 6, 9, 1, 7, 7, 3, 7, 8, 7, 5, 7, 8, 9, 3, 8, 7, 9, 5, 3, 9, 9, 1, 5, 4, 5, 1, 7, 3, 1, 7, 8, 6, 1, 8, 4, 6, 8, 6, 5, 5, 9, 2, 6, 1, 5, 9, 8, 7, 2, 8, 8, 3, 2, 3, 9, 8, 2, 8, 4, 6, 1, 9, 4

Offset: 1

Paul D. Hanna, Aug 27 2005

nonn

			G.f.: A(x) = x + 9*x^2 + 9*x^3 + 9*x^4 + 6*x^5 + 6*x^6 + 3*x^7 +...
then A(x) = B(B(B(B(B(B(B(B(B(x))))))))) where
B(x) = x + x^2 - 7*x^3 + 81*x^4 - 1122*x^5 + 16906*x^6 +...
is the g.f. of A112119.

Cf. A112119, A112104-A112117, A112120-A112127.

{a(n,m=9)=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)))}

A112119 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (9th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,9}, with B(0) = 0.

Original entry on oeis.org

1, 1, -7, 81, -1122, 16906, -264109, 4150081, -64119406, 955386299, -13491950523, 178108552187, -2193288809125, 25965294143459, -320197330438145, 4331428366450929, -54509980572007649, 309687851858995853, 8841175049606909354, -260481122023484957344, 727627679068983588258

Offset: 1

Paul D. Hanna, Aug 27 2005

sign

			A(x) = x + x^2 - 7*x^3 + 81*x^4 - 1122*x^5 + 16906*x^6 +...
where A(A(A(A(A(A(A(A(A(x))))))))) =
x + 9*x^2 + 9*x^3 + 9*x^4 + 6*x^5 + 6*x^6 + 3*x^7 +...
is the g.f. of A112118.

Cf. A112118, A112104-A112117, A112120-A112127.

{a(n,m=9)=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)))}

A112120 Unique sequence of numbers {1,2,3,...,10} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (10th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

Original entry on oeis.org

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

Offset: 1

Paul D. Hanna, Aug 27 2005

nonn

			G.f.: A(x) = x + 10*x^2 + 10*x^3 + 5*x^4 + 10*x^5 + 5*x^6 +...
then A(x) = B(B(B(B(B(B(B(B(B(B(x)))))))))) where
B(x) = x + x^2 - 8*x^3 + 104*x^4 - 1619*x^5 + 27437*x^6 +...
is the g.f. of A112121.

Cf. A112121, A112104-A112119, A112122-A112127.

{a(n,m=10)=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)))}

A112121 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (10th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,10}, with B(0) = 0.

Original entry on oeis.org

1, 1, -8, 104, -1619, 27437, -482626, 8553639, -149434331, 2527339944, -40748011084, 619534898788, -8892967520397, 124088656925363, -1797865061490547, 28140512084643142, -424643873334235802, 4269156014010214570, 19251023484926369328, -1456780704021544219838

Offset: 1

Paul D. Hanna, Aug 27 2005

sign

			A(x) = x + x^2 - 8*x^3 + 104*x^4 - 1619*x^5 + 27437*x^6 +...
where A(A(A(A(A(A(A(A(A(A(x)))))))))) =
x + 10*x^2 + 10*x^3 + 5*x^4 + 10*x^5 + 5*x^6 + 8*x^7 +...
is the g.f. of A112120.

Cf. A112120, A112104-A112119, A112122-A112127.

{a(n,m=10)=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)))}

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.

Original entry on oeis.org

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)))}

A112123 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (11th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,11}, with B(0) = 0.

Original entry on oeis.org

1, 1, -9, 131, -2279, 43161, -849269, 16866851, -331093879, 6316647841, -115528321709, 2007845708091, -33238536213650, 537616162919975, -8956186512464320, 158920634214746905, -2786226293720310297, 38547971903938600271, -198392033014273765511

Offset: 1

Paul D. Hanna, Aug 27 2005

sign

			A(x) = x + x^2 - 9*x^3 + 131*x^4 - 2279*x^5 + 43161*x^6 - 849269*x^7 +...
where A(A(A(A(A(A(A(A(A(A(A(x))))))))))) =
x + 11*x^2 + 11*x^3 + 11*x^4 + 11*x^5 + 11*x^6 + 11*x^7 +...
is the g.f. of A112122.

Cf. A112122, 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); return(polcoeff(F,n,x)))}

cp's OEIS Frontend

A112113 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (6th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,6}, with B(0) = 0.

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A112114 Unique sequence of numbers {1,2,3,...,7} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (7th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

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A112115 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (7th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,7}, with B(0) = 0.

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A112116 Unique sequence of numbers {1,2,3,...,8} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (8th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

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A112118 Unique sequence of numbers {1,2,3,...,9} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (9th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

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A112119 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (9th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,9}, with B(0) = 0.

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A112120 Unique sequence of numbers {1,2,3,...,10} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (10th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

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A112121 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (10th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,10}, with B(0) = 0.

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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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A112123 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (11th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,11}, with B(0) = 0.

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