A215119
G.f. A(x) satisfies: A(A(A(A(A(x))))) = G(x) where G(x) = x + 4*x^2 + x*G(G(G(G(G(x))))) is the g.f. of A215118.
Original entry on oeis.org
1, 1, 1, 101, 2301, 82601, 3287001, 149411501, 7474902101, 406765054801, 23836604715601, 1493376284080501, 99459838574595501, 7009748111184956601, 520845172037612209801, 40672220108202107951101, 3328819620490715884626501, 284871268231239093741932001
Offset: 1
G.f.: A(x) = x + x^2 + x^3 + 101*x^4 + 2301*x^5 + 82601*x^6 + 3287001*x^7 +...
Let G(x) = A(A(A(A(A(x))))):
G(x) = x + 5*x^2 + 25*x^3 + 625*x^4 + 18125*x^5 + 628125*x^6 + 25390625*x^7 +...
such that G(x) = x + 4*x^2 + x*G(G(G(G(G(x))))):
G(G(G(G(G(x))))) = x + 25*x^2 + 625*x^3 + 18125*x^4 + 628125*x^5 + 25390625*x^6 +...
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{a(n)=local(A=x+x^2,B=x+4*x^2);for(i=1,n+1,B=x+4*x^2+x*subst(B,x,subst(B,x,subst(B,x,subst(B,x,B+x^2*O(x^n))))));
for(j=1, n+1, A=round((4*A+subst(B, x, serreverse(subst(A,x,subst(A,x,subst(A,x,A+x^2*O(x^n)))))))/5));; polcoeff(A, n)}
for(n=1, 31, print1(a(n), ", "))
A213010
G.f. satisfies: A(x) = x+x^2 + x*A(A(x)).
Original entry on oeis.org
1, 2, 4, 16, 80, 480, 3296, 25152, 209600, 1884160, 18110080, 184898304, 1994964736, 22654449664, 269855506944, 3362350046208, 43715434232832, 591812683833344, 8326660788725760, 121550217508892672, 1838089917983911936, 28753297176215257088, 464675647688625364992
Offset: 1
G.f.: A(x) = x + 2*x^2 + 4*x^3 + 16*x^4 + 80*x^5 + 480*x^6 + 3296*x^7 +...
where
A(A(x)) = x + 4*x^2 + 16*x^3 + 80*x^4 + 480*x^5 + 3296*x^6 +...
Related expansions.
Let B(B(x)) = A(x), then B(x) is an integer series:
B(x) = x + x^2 + x^3 + 5*x^4 + 21*x^5 + 125*x^6 + 825*x^7 + 6133*x^8 +...
where the coefficients of B(x) are congruent to 1 modulo 4.
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{a(n)=local(A=x+2*x^2);for(i=1,n,A=x+x^2+x*subst(A,x,A+x*O(x^n)));polcoeff(A,n)}
for(n=1,31,print1(a(n),", "))
A215116
G.f. satisfies: A(x) = x + 3*x^2 + x*A(A(A(A(x)))).
Original entry on oeis.org
1, 4, 16, 256, 4864, 111616, 2983936, 89743360, 2970861568, 106768629760, 4125849419776, 170207219286016, 7454572671926272, 345078981839552512, 16822127738969128960, 860944587541763325952, 46137178395559050870784, 2582843669636660403896320, 150735442996358913332346880
Offset: 1
G.f.: A(x) = x + 4*x^2 + 16*x^3 + 256*x^4 + 4864*x^5 + 111616*x^6 + 2983936*x^7 +...
where
A(A(A(A(x)))) = x + 16*x^2 + 256*x^3 + 4864*x^4 + 111616*x^5 + 2983936*x^6 +...
Related expansions.
Let D(D(D(D(x)))) = A(x), then D(x) is an integer series where:
D(x) = x + x^2 + x^3 + 49*x^4 + 721*x^5 + 17281*x^6 + 452065*x^7 +...
where the coefficients of D(x) are congruent to 1 modulo 48.
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{a(n)=local(A=x+4*x^2); for(i=1,n,A=x+3*x^2+x*subst(A,x,subst(A,x,subst(A,x,A+x*O(x^n))))); polcoeff(A, n)}
for(n=1, 31, print1(a(n), ", "))
A215114
G.f. satisfies: A(x) = x + 2*x^2 + x*A(A(A(x))).
Original entry on oeis.org
1, 3, 9, 81, 891, 11907, 184437, 3199581, 60932007, 1257133527, 27836230041, 656867748537, 16429561047891, 433686821472747, 12038953175046909, 350402975398982133, 10665927632978564895, 338769129913521564735, 11205026468737167058785
Offset: 1
G.f.: A(x) = x + 3*x^2 + 9*x^3 + 81*x^4 + 891*x^5 + 11907*x^6 + 184437*x^7 +...
where
A(A(A(x))) = x + 9*x^2 + 81*x^3 + 891*x^4 + 11907*x^5 + 184437*x^6 +...
Related expansions.
Let C(C(C(x))) = A(x), then C(x) is an integer series where:
C(x) = x + x^2 + x^3 + 19*x^4 + 163*x^5 + 2269*x^6 + 34093*x^7 +...
where the coefficients of C(x) are congruent to 1 modulo 9.
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{a(n)=local(A=x+3*x^2); for(i=1, n, A=x+2*x^2+x*subst(A, x, subst(A, x, A+x*O(x^n)))); polcoeff(A, n)}
for(n=1, 31, print1(a(n), ", "))
Showing 1-4 of 4 results.
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