A382367 -id:A382367 - cp's OEIS frontend

A382372 Expansion of 1/( 1 - Sum_{k>=0} x^(4^k) / (1 - x^(4^k)) ).

1, 1, 2, 4, 9, 18, 37, 76, 158, 325, 670, 1381, 2850, 5876, 12117, 24986, 51530, 106262, 219131, 451885, 931876, 1921695, 3962884, 8172182, 16852538, 34752996, 71667001, 147790386, 304770689, 628492615, 1296066140, 2672724207, 5511643710, 11366012289

Offset: 0

Seiichi Manyama, Mar 23 2025

nonn

Cf. A327736, A382367, A382373, A382378.

Cf. A115362.

a(0) = 1; a(n) = Sum_{k=1..n} A115362(k-1) * a(n-k).
G.f.: 1/(1 - Sum_{i>=1, j>=0} x^(i*4^j)).
G.f. A(x) satisfies A(x) = 1/( 1/A(x^4) - x/(1-x) ).

A382373 Expansion of 1/( 1 - Sum_{k>=0} x^(5^k) / (1 - x^(5^k)) ).

Original entry on oeis.org

1, 1, 2, 4, 8, 17, 34, 69, 140, 284, 578, 1173, 2382, 4837, 9822, 19948, 40508, 82261, 167050, 339233, 688896, 1398964, 2840926, 5769169, 11715654, 23791402, 48314044, 98113049, 199241660, 404607125, 821650100, 1668554099, 3388392198, 6880928638, 13973346686

Offset: 0

Seiichi Manyama, Mar 23 2025

nonn

Cf. A327736, A382367, A382372, A382378.

Cf. A055457.

a(0) = 1; a(n) = Sum_{k=1..n} A055457(k) * a(n-k).
G.f.: 1/(1 - Sum_{i>=1, j>=0} x^(i*5^j)).
G.f. A(x) satisfies A(x) = 1/( 1/A(x^5) - x/(1-x) ).

A382378 Expansion of 1/( 1 - Sum_{k>=0} x^(6^k) / (1 - x^(6^k)) ).

Original entry on oeis.org

1, 1, 2, 4, 8, 16, 33, 66, 133, 268, 540, 1088, 2194, 4421, 8910, 17957, 36190, 72936, 146996, 296252, 597061, 1203306, 2425121, 4887544, 9850272, 19852060, 40009486, 80634401, 162509126, 327517977, 660073866, 1330301036, 2681064864, 5403370072, 10889855193, 21947218962

Offset: 0

Seiichi Manyama, Mar 23 2025

nonn

Cf. A327736, A382367, A382372, A382373.

Cf. A122841, A373216.

a(0) = 1; a(n) = Sum_{k=1..n} A373216(k) * a(n-k).
G.f.: 1/(1 - Sum_{i>=1, j>=0} x^(i*6^j)).
G.f. A(x) satisfies A(x) = 1/( 1/A(x^6) - x/(1-x) ).

A382368 Expansion of 1/( 1 - 4 * Sum_{k>=0} x^(3^k) / (1 - x^(3^k)) )^(1/2).

Original entry on oeis.org

1, 2, 8, 36, 162, 750, 3536, 16858, 81100, 392914, 1914268, 9369190, 46032396, 226898158, 1121510176, 5556731592, 27589816042, 137240945530, 683808343416, 3412128301538, 17048743841882, 85286538527304, 427112389604968, 2141096012912290, 10743017708448232

Offset: 0

Seiichi Manyama, Mar 22 2025

nonn

Cf. A382367, A382369.

G.f. A(x) satisfies A(x) = 1/( 1/A(x^3)^2 - 4*x/(1-x) )^(1/2).

A382369 Expansion of 1/( 1 - 9 * Sum_{k>=0} x^(3^k) / (1 - x^(3^k)) )^(1/3).

Original entry on oeis.org

1, 3, 21, 168, 1416, 12396, 111219, 1015221, 9386643, 87650775, 824926152, 7813623234, 74403686022, 711670543635, 6833183666862, 65826593737206, 635962416394296, 6159757277793783, 59796182640515031, 581643107427461664, 5667929195670139296, 55322424966010598556

Offset: 0

Seiichi Manyama, Mar 22 2025

nonn

Cf. A382367, A382368.

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

cp's OEIS Frontend

A382372 Expansion of 1/( 1 - Sum_{k>=0} x^(4^k) / (1 - x^(4^k)) ).

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A382373 Expansion of 1/( 1 - Sum_{k>=0} x^(5^k) / (1 - x^(5^k)) ).

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A382378 Expansion of 1/( 1 - Sum_{k>=0} x^(6^k) / (1 - x^(6^k)) ).

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A382368 Expansion of 1/( 1 - 4 * Sum_{k>=0} x^(3^k) / (1 - x^(3^k)) )^(1/2).

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A382369 Expansion of 1/( 1 - 9 * Sum_{k>=0} x^(3^k) / (1 - x^(3^k)) )^(1/3).

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Author

Keywords

Crossrefs

Formula