A223142 -id:A223142 - cp's OEIS frontend

A223143 G.f. satisfies: A(x)^3 = A(x^2)^3 + 9*x.

1, 3, -6, 27, -141, 819, -5022, 31968, -209202, 1398420, -9505854, 65499759, -456410943, 3210397173, -22763553876, 162524220984, -1167359075781, 8429107868541, -61148608627518, 445450238075655, -3257116365714831, 23896262127268719, -175854177039133998

Offset: 0

Paul D. Hanna, Mar 15 2013

sign

			G.f.: A(x) = 1 + 3*x - 6*x^2 + 27*x^3 - 141*x^4 + 819*x^5 - 5022*x^6 +...
where
A(x)^3 = 1 + 9*x + 9*x^2 + 9*x^4 + 9*x^8 + 9*x^16 + 9*x^32 +...+ 9*x^(2^n) +...

Paul D. Hanna, Table of n, a(n) for n = 0..300

Cf. A223142, A107086, A223026.

{a(n)=local(A=1+x); for(i=1, #binary(n), A=(subst(A, x, x^2)^3+9*x+x*O(x^n))^(1/3)); polcoeff(A, n, x)}
for(n=0,30,print1(a(n),", "))

G.f.: A(x) = ( 1 + Sum_{n>=0} 9*x^(2^n) )^(1/3).

A382187 Expansion of 1/(1 - 4 * Sum_{k>=0} x^(2^k))^(1/2).

Original entry on oeis.org

1, 2, 8, 32, 138, 604, 2696, 12176, 55512, 254888, 1177064, 5461040, 25435296, 118856272, 556962928, 2616287392, 12315914698, 58084552572, 274395134600, 1298187523792, 6150051540460, 29170558879736, 138512004786624, 658362443599296, 3132140164624680

Offset: 0

Seiichi Manyama, Mar 18 2025

Cf. A023359, A382188.

Cf. A223142.

G.f. A(x) satisfies A(x) = 1/(1/A(x^2)^2 - 4*x)^(1/2).

A382333 Expansion of ( 1 + 4 * Sum_{k>=0} x^(2^k)/(1 - x^(2^k)) )^(1/2).

Original entry on oeis.org

1, 2, 2, -2, 8, -10, 6, 26, -108, 258, -342, -194, 2700, -8994, 17830, -12878, -61910, 322110, -860106, 1284546, 571880, -10749654, 38883554, -82867578, 68869212, 286234558, -1619591538, 4559780610, -7250287740, -2206074398, 59250601986, -225063455922

Offset: 0

Seiichi Manyama, Mar 22 2025

Cf. A001511, A382334.

Cf. A223142, A382335.

G.f. A(x) satisfies A(x) = ( A(x^2)^2 + 4*x/(1-x) )^(1/2).

A382335 Expansion of ( 1 + 4 * Sum_{k>=0} x^(2^k)/(1 - x^(2^k))^2 )^(1/2).

Original entry on oeis.org

1, 2, 4, -2, 10, -2, -20, 82, -108, -114, 1052, -2702, 2054, 11394, -52636, 99534, 32938, -831698, 2649676, -3119694, -8779530, 54334130, -125649628, 31877726, 849214460, -3274210670, 5129552132, 7097067566, -65583106070, 180299051838, -133300439300

Offset: 0

Seiichi Manyama, Mar 22 2025

Cf. A129527, A382336.

Cf. A223142, A382333.

G.f. A(x) satisfies A(x) = ( A(x^2)^2 + 4*x/(1-x)^2 )^(1/2).

A382196 Expansion of (1 + 9 * Sum_{k>=0} x^(3^k))^(1/3).

Original entry on oeis.org

1, 3, -9, 48, -288, 1917, -13563, 99927, -758079, 5879757, -46401705, 371337021, -3005974710, 24568145019, -202442064183, 1679864383800, -14024716370064, 117715927282470, -992725129013121, 8407191323492226, -71467963130581758, 609605555349330009

Offset: 0

Seiichi Manyama, Mar 18 2025

This sequence is different from A298308.

Cf. A223142, A223143, A298308, A382190.

G.f. A(x) satisfies A(x) = (A(x^3)^3 + 9*x)^(1/3).

cp's OEIS Frontend

A223143 G.f. satisfies: A(x)^3 = A(x^2)^3 + 9*x.

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A382187 Expansion of 1/(1 - 4 * Sum_{k>=0} x^(2^k))^(1/2).

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A382333 Expansion of ( 1 + 4 * Sum_{k>=0} x^(2^k)/(1 - x^(2^k)) )^(1/2).

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A382335 Expansion of ( 1 + 4 * Sum_{k>=0} x^(2^k)/(1 - x^(2^k))^2 )^(1/2).

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A382196 Expansion of (1 + 9 * Sum_{k>=0} x^(3^k))^(1/3).

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