cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A382367 Expansion of 1/( 1 - Sum_{k>=0} x^(3^k) / (1 - x^(3^k)) ).

Original entry on oeis.org

1, 1, 2, 5, 10, 21, 46, 97, 206, 442, 940, 2002, 4272, 9103, 19400, 41360, 88156, 187901, 400534, 853747, 1819782, 3878965, 8268160, 17623888, 37566072, 80073580, 170680002, 363811370, 775478548, 1652963605, 3523358532, 7510180375, 16008251264, 34122231512
Offset: 0

Views

Author

Seiichi Manyama, Mar 22 2025

Keywords

Crossrefs

Cf. A327736, A382372, A382373, A382378.
Cf. A382368, A382369.
Cf. A051064.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A051064(k) * a(n-k).
G.f.: 1/(1 - Sum_{i>=1, j>=0} x^(i*3^j)).
G.f. A(x) satisfies A(x) = 1/( 1/A(x^3) - x/(1-x) ).

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

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Mar 23 2025

Keywords

Crossrefs

Cf. A327736, A382367, A382373, A382378.
Cf. A115362.

Formula

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

Views

Author

Seiichi Manyama, Mar 23 2025

Keywords

Crossrefs

Cf. A327736, A382367, A382372, A382378.
Cf. A055457.

Formula

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

Views

Author

Seiichi Manyama, Mar 23 2025

Keywords

Crossrefs

Cf. A327736, A382367, A382372, A382373.
Cf. A122841, A373216.

Formula

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) ).

A382365 Expansion of 1/( 1 - 4 * Sum_{k>=0} x^(2^k) / (1 - x^(2^k)) )^(1/2).

Original entry on oeis.org

1, 2, 10, 46, 232, 1174, 6078, 31786, 167836, 892258, 4770466, 25622286, 138146540, 747253022, 4053224974, 22038282338, 120079277626, 655486778654, 3584062901182, 19625809294386, 107610733877720, 590751275348362, 3246588926918074, 17860031073624694
Offset: 0

Views

Author

Seiichi Manyama, Mar 22 2025

Keywords

Crossrefs

Cf. A327736, A382366.
Cf. A382187.

Formula

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

A382366 Expansion of 1/( 1 - 9 * Sum_{k>=0} x^(2^k) / (1 - x^(2^k)) )^(1/3).

Original entry on oeis.org

1, 3, 24, 201, 1818, 17004, 163068, 1590798, 15718899, 156860076, 1577644998, 15969030780, 162498057048, 1660951840611, 17042090466264, 175436835017475, 1811209862304735, 18746380864328061, 194465530800628908, 2021343414865754583, 21048513676138546848
Offset: 0

Views

Author

Seiichi Manyama, Mar 22 2025

Keywords

Crossrefs

Cf. A327736, A382365.
Cf. A382188.

Formula

G.f. A(x) satisfies A(x) = 1/( 1/A(x^2)^3 - 9*x/(1-x) )^(1/3).
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.