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 1-3 of 3 results.

A373278 Expansion of 1 / ( (1 - 9*x^3) * (1 - x/(1 - 9*x^3)^(1/3)) ).

Original entry on oeis.org

1, 1, 1, 10, 13, 16, 100, 148, 205, 1000, 1606, 2410, 10000, 17005, 27070, 100000, 177421, 295648, 1000000, 1833178, 3168538, 10000000, 18811948, 33503020, 100000000, 192080866, 350707345, 1000000000, 1953820210, 3642942040, 10000000000, 19815499120, 37611477133
Offset: 0

Views

Author

Seiichi Manyama, Jun 11 2024

Keywords

Crossrefs

Cf. A000079, A100095, A373583, A373621.
Cf. A011557, A371458.

Programs

  • PARI
    a(n) = sum(k=0, n\3, 9^k*binomial(n/3, k));

Formula

a(3*n) = 10^n for n >= 0.
a(n) = Sum_{k=0..floor(n/3)} 9^k * binomial(n/3,k).
a(n) == 1 (mod 3).
D-finite with recurrence (n-1)*(n-2)*a(n) +2*(-14*n^2+69*n-91)*a(n-3) +9*(n-3)*(29*n-114)*a(n-6) -810*(n-3)*(n-6)*a(n-9)=0. - R. J. Mathar, Jun 21 2024

A373621 Expansion of 1 / ( (1 - 25*x^5) * (1 - x/(1 - 25*x^5)^(1/5)) ).

Original entry on oeis.org

1, 1, 1, 1, 1, 26, 31, 36, 41, 46, 676, 881, 1111, 1366, 1646, 17576, 24281, 32386, 42016, 53296, 456976, 658806, 916411, 1238666, 1635071, 11881376, 17706456, 25462936, 35569066, 48496846, 308915776, 472880356, 698851961, 1003283216, 1405555496, 8031810176
Offset: 0

Views

Author

Seiichi Manyama, Jun 11 2024

Keywords

Crossrefs

Cf. A000079, A100095, A373278, A373583.
Cf. A373510.

Programs

  • PARI
    a(n) = sum(k=0, n\5, 25^k*binomial(n/5, k));

Formula

a(5*n) = 26^n for n >= 0.
a(n) = Sum_{k=0..floor(n/5)} 25^k * binomial(n/5,k).
a(n) == 1 (mod 5).

A373627 Expansion of 1 / ( (1 - 8*x^4) * (1 - x/(1 - 8*x^4)^(1/4)) ).

Original entry on oeis.org

1, 1, 1, 1, 9, 11, 13, 15, 81, 109, 141, 177, 729, 1041, 1429, 1901, 6561, 9759, 13981, 19419, 59049, 90483, 133893, 192327, 531441, 832911, 1264173, 1865539, 4782969, 7628799, 11816853, 17828163, 43046721, 69620541, 109646397, 168500385, 387420489, 633634769
Offset: 0

Views

Author

Seiichi Manyama, Jun 11 2024

Keywords

Crossrefs

Cf. A373509, A373583.

Programs

  • PARI
    a(n) = sum(k=0, n\4, 8^k*binomial(n/4, k));

Formula

a(4*n) = 9^n for n >= 0.
a(n) = Sum_{k=0..floor(n/4)} 8^k * binomial(n/4,k).
a(n) == 1 (mod 2).
Showing 1-3 of 3 results.

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

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